Jonathan M. Rosenberg
Primary research areas:
Representation theory of Lie groups, C*algebras,
Ktheory, topology and geometry of manifolds, index theory of
elliptic operators, noncommutative geometry,
related areas of mathematical physics.
Some old publications now available on the web:
 (with Calvin C. Moore) Comments on a
paper of I. D. Brown and Y. Guivarc'h,
Annales Scientifiques de
l'École Normale Supérieure (4) 8 (1975), 379381.
(For the BrownGuivarc'h paper itself,
see
here.)
 The
C*algebras of some real and padic solvable groups,
Pacific J. Math. 65 (1976), no. 1, 175192.
 Frobenius reciprocity for squareintegrable
factor representations,
Illinois Journal of Mathematics 21 (1977), no. 4, 818825.
 A
Quick Proof of HarishChandra's Plancherel Theorem for Spherical
Functions on a Semisimple Lie Group, Proc. Amer. Math. Soc. 63
(1977), 143149.
 Remarks
on random walks on semi simple Lie groups,
Mémoires de la Société Mathématique
de France 54 (1977), 119127.
 Amenability
of crossed products of C*algebras, Comm. Math. Phys. 57 (1977), no. 2, 187191.
 (with Edward Effros)
C*algebras with approximately inner flip, Pacific J. Math. 77 (1978), no. 2, 417443.
 SquareIntegrable
Factor Representations of Locally Compact Groups,
Trans. Amer. Math. Soc. 237 (1978), 133.
 Appendix
to "Crossed products of UHF algebras by
product type actions" by Ola Bratteli, Duke Math. J. 46 (1979), no. 1,
2526.
 (with E. Gootman) The structure of crossed product C*algebras:
a proof of the generalized EffrosHahn conjecture,
Invent. Math. 52 (1979), no. 3, 283298.
 Realization
of SquareIntegrable Representations of Unimodular Lie Groups on
L^{2}Cohomology Spaces,
Trans. Amer. Math. Soc. 261 (1980), 132.
 (with Claude Schochet) The classification of extensions of C*algebras,
Bull. Amer. Math. Soc. (N.S.) 4 (1981), no. 1, 105110.
 (with Claude Schochet)
Comparing
functors classifying extensions of C*algebras, J. Operator Theory 5 (1981),
no. 2, 267282.
 (with Richard Herman)
Normclose
group actions on C*algebras, J. Operator Theory 6 (1981), no. 1,
2537.

The role of Ktheory in noncommutative algebraic
topology, in Operator algebras and Ktheory (San Francisco,
Calif., 1981), pp. 155182, Contemp. Math., 10, Amer. Math. Soc., Providence,
R.I., 1982.

C*algebras,
positive scalar curvature, and the Novikov
conjecture, Publ. Math. IHES 58 (1983), 197212.
 C*algebras, positive scalar
curvature and the Novikov conjecture. II in
Geometric methods in operator algebras (Kyoto, 1983), 341374,
Pitman Res. Notes Math. Ser., 123, Longman Sci. Tech., Harlow, 1986.
 Group C*algebras and topological invariants,
Operator algebras and group representations, Vol. II (Neptun, 1980), 95115,
Monogr. Stud. Math., 18, Pitman, Boston, MA, 1984.
 Some results on cohomology with Borel cochains,
with applications to group actions on operator algebras,
Operator Theory: Advances and Applications, vol. 17,
Birkhäuser, 1986, pp. 301330.
 (with Steven Hurder, Dorte Olesen, and Iain Raeburn)
The Connes spectrum for actions of
abelian groups on continuoustrace algebras,
Ergodic Thy. and Dyn. Systems 6 (1986), no. 4, 541560.
 C*algebras, positive scalar curvature,
and the Novikov conjecture, III, Topology 25, no. 3 (1986), 319336.
 (with Claude Schochet) The
Künneth theorem and the universal coefficient theorem
for Kasparov's generalized Kfunctor,
Duke Math. J. 55, no. 2 (1987), 431474.
 (with Claude Schochet)
The Künneth Theorem and the Universal Coefficient Theorem for
Equivariant KTheory and KKTheory, Mem. Amer. Math. Soc. no. 348,
1986. A copy is also available here.
 Quasidiagonality and nuclearity (appendix to a paper of D. Hadwin),
J. Operator Theory 18 (1987), 1518.
 Applications of analysis on Lipschitz manifolds, Miniconferences on harmonic analysis and operator algebras,
Proc. Centre for Mathematical Analysis, Austral. Nat. Univ., vol. 16,
1988.
 (with Iain Raeburn) Crossed
Products of ContinuousTrace C*Algebras by Smooth Actions,
Trans. Amer. Math. Soc. 305 (1988), 145.
 ContinuousTrace Algebras
from the Bundle Theoretic Point of View,
J. Australian Math. Soc. (Ser. A) 47 (1989), 368381.
 (with Roger Howe) The unitary
representation theory of GL(n) of an infinite discrete field,
Israel J. Math. 67 (1989), no. 1, 6781.
 (with Shmuel Weinberger) An equivariant
Novikov conjecture, With an appendix by J. P. May, KTheory
4 (1990), no. 1, 2953.
 The KOassembly map
and positive scalar curvature, in
Algebraic topology, Poznan, 1989, 170182,
Lecture Notes in Math., 1474, Springer, Berlin, 1991.
 (with Shmuel Weinberger) Higher Gsignatures
for Lipschitz manifolds, KTheory 7 (1993), 101132.
 C*algebras and Mackey's theory of
group representations (in "C*algebras: 19431993 [San Antonio, TX,
1993]", Contemp. Math., 167, Amer. Math. Soc., 1994.)
 (with Siegfried Echterhoff)
Fine structure of the Mackey machine for actions of abelian groups
with constant Mackey obstruction,
Pacific J. Math. 170, no. 1 (1995), 1752.
 (with Shmuel Weinberger) Higher
Gindices and applications, Annales Scientifiques de
l'École Normale Supérieure (4) 21 (1998), 479495.
 BrownDouglasFillmore
theory, an article from the Encyclopaedia of Mathematics
(2002).
Some recent publications:
 "Algebraic KTheory and its Applications," Graduate Texts in
Mathematics, vol. 147,
SpringerVerlag, New York,
1994 (approx. 400 pages). ISBN 0387942483.
Corrected second printing, 1996. For owners of the first printing, here
is a list of the mistakes and misprints
(in dvi format)
that have been corrected in the second printing. This list is
also available in pdf format.
For owners of both
printings, here are some additional errata
in dvi format or in pdf format.
 "Novikov Conjectures, Index Theorems and Rigidity," coedited
with Steve Ferry and Andrew Ranicki, London Math. Soc. Lecture Notes,
vols. 226 and 227 (approx. 380 pages each),
Cambridge Univ. Press,
1995. ISBN 0521497965 and ISBN 0521497957. Some
errata are available.
 (with Stephan Stolz),
"A "stable" version of the GromovLawson conjecture," in "The Čech Centennial: A Conference on Homotopy Theory," M. Cenkl
and H. Miller, eds., Contemp. Math., vol. 181, Amer. Math. Soc., 1995,
pp. 405418.
 (with Ronald L. Lipsman),
"The behavior of Fourier transforms on nilpotent
Lie groups," Trans. Amer. Math. Soc. 384 (1996), 10311050.
 "Lajos Pukánszky: In memorium,"
Notices Amer. Math. Soc. 45 (1998), 492. The whole
collection of memorial articles in this issue of the Notices is
available
here.
 "The algebraic Ktheory of operator
algebras." Appeared in KTheory 12 (1997), 7599.
The dvi file uses the xypicfonts. The paper is also
available in postscript format (approx. 290kb).
 a "featured review" of papers by
Nest and Tsygan on algebraic index theorems, Math. Rev. 96j:58163ab.
 "Behavior of Ktheory under
quantization," in Operator Algebras and
Quantum Field Theory, ed. by S. Doplicher, R. Longo,
J. E. Roberts, and L. Zsido, International Press, 1997, pp.
404415. The paper is also
available in postscript format (approx. 160kb).
 "Reflections on C. T. C.
Wall's work on cobordism." appeared in
"Surveys on Surgery
Theory", vol. 2, Ann. of Math. Studies, vol. 149.
 Notes for lectures at the
Summer Research Conference on Algebraic KTheory at Seattle in July,
1997. A more complete version
that appeared in the
proceedings of the conference, PSPUM/67, AMS, 1999, pp. 231248,
is also available.
 "The Khomology class of the
Euler characteristic operator is trivial,"
Proc. Amer. Math. Soc.
127 (1999), pp. 34673474.
 (with Stephan Stolz), "Metrics of
positive scalar curvature and connections with surgery."
appeared in "Surveys
on Surgery Theory", vol. 2, Ann. of Math. Studies, vol. 149.
 "The Khomology class of the
equivariant Euler characteristic operator." The paper is also
available in postscript format
(approx. 230kb). This paper is now obsolete; see item #27 below.
 "The GSignature Theorem
Revisited." Appeared in
Tel
Aviv Topology Conference: Rothenberg
Festschrift, M. Farber, W. Lück, and S. Weinberger, eds.,
Contemp. Math. 231, Amer. Math. Soc., 1999, pp. 251264.
The paper is also
available in pdf format (approx. 280kb).
 "Surgery
theory today: what it is and where it's going."
appeared in "Surveys
on Surgery Theory", vol. 2, Ann. of Math. Studies, vol. 149.
 A review of Characters of Connected
Lie groups by Lajos Pukánszky, appeared in the book reviews section
of the Bulletin of the London Math. Soc, 2001.
 A minicourse on applications of
noncommutative geometry to topology, slides for lectures at the
CMI Instructional
Symposium and AMS
Summer Research Conference
on Noncommutative Geometry at Mount Holyoke
College, June, 2000. (pdf format, approx 900kb)
 A history of noncommutative
harmonic analysis in 20th century Hungarian mathematics, for
A
Panorama of Hungarian Mathematics in the XXth Century, edited
by John Horvath, published by Springer, 2006, in the
series "Bolyai Society Mathematical Studies". (pdf format, approx 250kb)

A Guide to
MATLAB, for Beginners and Experienced Users, Cambridge
University Press, 2001. 2nd edition in press, 2005.
 Some examples of mathematical analysis
applied to Talmud study. Some of this article is in Hebrew, but
most of the important sections are translated. To have the Hebrew
display correctly, set the font encoding to "Hebrew visual",
ISO88598.
 The Yamabe invariant for nonsimply
connected manifolds, with Boris Botvinnik,
Journal of
Differential Geometry 62 (2002), no. 2, 175208.
(pdf format, approx 280kb)
 Groupoid C*algebras and index theory on
manifolds with singularities (PDF format, approx 220kb),
Geometriae
Dedicata 100 (2003), no. 1, 6584.
A lecture
on this material is also available on the MSRI website in streaming
video (with the slides in a separate window).
 Preliminary copy of several chapters of a
book on noncommutative geometry applied to topology, based on
item 17 above.
 Slides from a talk at the
Varieties
Conference in honor of Blaine Lawson, June, 2002, on "Recent progress on
the GromovLawson Conjecture".
 Positive scalar
curvature for manifolds with elementary abelian fundamental group
(pdf format, approx 175kb), with Boris Botvinnik,
Proceedings of the Amer. Math. Soc. 133 (2005), no. 2, 545556.
Also available as a
dvi file.
 The equivariant Lefschetz fixed point theorem
for proper cocompact Gmanifolds (pdf format, approx 300kb),
with Wolfgang Lück, Proc. Trieste Conf. on HighDimensional
Manifolds, 2001, T. Farrell, L. Göttsche, and W. Lück, eds.,
World Scientific, 2003.
 Equivariant Euler characteristics and
Khomology Euler classes for proper cocompact Gmanifolds
(pdf format, approx 380kb),
with Wolfgang Lück, Geometry and
Topology 7 (2003), 569613.
Also available in postscript format.
 Slides for a talk on "A selective
history of the Stonevon Neumann theorem" at the AMS meeting in
Baltimore, January, 2003 (special session in honor of the 100th birthdays
of Stone and von Neumann). A more detailed version is available
as item #31 below.
 Slides for a talk on "Another look at
the Universal Coefficient Theorem for Ext" at the AMS meeting in
Baltimore, January, 2003 (special session in honor of Larry Brown's 60th
birthday).
 Ktheory and geometric topology,
a survey article from the "Handbook of Algebraic
Ktheory", edited by Eric Friedlander and Dan Grayson,
Springer, 2004, pp. 577610. Published version
now available online.
 A Selective History of the
Stonevon Neumann Theorem (pdf format, approx 340kb), in
Operator algebras, quantization, and noncommutative geometry,
Contemp. Math., 365, Amer. Math. Soc., Providence, RI, 2004, pp. 123158.
 Tduality
for torus bundles via noncommutative topology, with Varghese Mathai,
Comm. Math. Physics 253 (2005), no. 3, 705721.
 The signature operator
at 2, with Shmuel Weinberger, Topology
45 (2006), no. 1, 4763.
 Comparison Between Algebraic and
Topological KTheory for Banach Algebras and
C*Algebras, a survey article from the "Handbook
of Algebraic Ktheory", edited by Eric Friedlander and Dan Grayson,
Springer, 2004, pp. 843874. Published version
now available online.
 A Ktheory perspective
on Tduality in string theory, slides for a talk at the
Great Lakes
Ktheory Conference, X. This talk is based on the
material of #32 above.
 On mysteriously missing Tduals,
Hflux and the Tduality group, with Varghese Mathai,
to appear in "Proceedings of the XXXIII International
Conference of Differential Geometric Methods in Mathematical Physics"
(August 2005), editors MoLin Ge and Weiping Zhang,
World Scientific 2006.
 Slides and
homework exercises from the
Oberwolfach
Seminar on Topological KTheory of Noncommutative
Algebras and Applications.
 Tduality for torus bundles with
Hfluxes via noncommutative topology, II: the highdimensional case
and the Tduality group, with Varghese Mathai,
Advances in Theoretical and Mathematical Physics 10 (2006),
no. 1, 123158.
 An analogue of the Novikov Conjecture
in complex algebraic geometry, Trans. Amer. Math. Soc.
360 (2008), no. 1, 383394.
 A review of The Novikov Conjecture:
Geometry and Algebra, by Matthias Kreck and Wolfang Lück,
Bull. Amer. Math. Soc. 43 (2006), 599604.
 Dbranes, RRfields and Duality on
Noncommutative Manifolds, with Jacek Brodzki, Varghese Mathai, and
Richard J. Szabo, Comm. Math. Physics 277 (2008),
no. 3, 643706.
 Manifolds of positive scalar curvature:
a progress report, in Surveys in Differential
Geometry, vol. XI: Metric and Comparison Geometry,
ed. by Jeffrey Cheeger and Karsten Grove.
 Applications of noncommutative topology
in geometry and string theory, informal notes from a course at the
Institut Henri Poincaré, January, 2007.
 The numbers in Numbers,
a statistical analysis of the census data in the Biblical book of Numbers.
Set the font encoding to Unicode (UTF16) if you want the Hebrew to
display properly.
 Notes from a talk at Oberwolfach on
#40 above.
 Slides from a talk at a Special
Session at the San Deigo AMS meeting, January 2008: "First steps
towards a noncommutative theory of nonlinear elliptic equations".
 Noncommutative
variations on Laplace's equation, based in part on #45 above,
in Analysis and PDE, 1
(2008), no. 1, 95114, arXiv:0802.4033.

Noncommutative correspondences, duality and Dbranes in bivariant Ktheory,
with Jacek Brodzki, Varghese Mathai, and Richard J. Szabo,
Adv. in Theoretical and
Math. Phys. 13 (2009), no. 2, 497552,
arXiv:0708.2648.
 The SCHOL
Project at the University of Maryland: Using Mathematical Software in the
Teaching of Sophomore Differential Equations, with Ronald L. Lipsman
and John E. Osborn, J. Numer. Anal. Indust. Appl. Math. 3, no. 12,
81103.
 A noncommutative sigmamodel,
with Varghese Mathai, J.
of Noncommutative Geometry 5 (2011), no. 2, 265294.
 Notes and slides from course at
the Buenos Aires Winter School on Noncommutative Geometry, JulyAugust
2010, to appear in Clay Math. Proc. 16 (2012), 93129.
 Introduction to Proc. Symp. Pure Math., vol. 81,
"Superstrings, geometry, topology, and C*algebras", Amer. Math. Soc., 2010.
 (with Stefan
MendezDiez) Ktheoretic matching of brane charges in S and
Uduality, arxiv:1007.1202, Adv. Theor. Math. Phys.
16 (2012), no. 6, 15911618.
 Slides from a lecture series at RIMS,
Kyoto, February, 2011, on Dualities in field theories and
the role of Ktheory.
 Dualities in
field theories and the role of Ktheory, arxiv:1107.5015,
appeared in
Noncommutative Geometry and Physics, 3, ed. by Giuseppe Dito
et al., World Scientific, 2013, 485506.
 Some work of Stefan Banach and
the mathematics it has generated,
Wiadomości Matematyczne 48 (2012),
no. 2, 217212. (Special issue about Polish mathematicians for the
6th European Congress of Mathematics, 2012.)
 The
Künneth Theorem in equivariant Ktheory for actions of a cyclic
group of order 2, Alg. and
Geom. Topology 13 (2013) 12251241, arXiv:1208.6355.
 (with
Yehoshua Dan Agassi) Flux quantization for a superconducting ring in
the shape of a Möbius band, arXiv:1301.2743.
 Slides
for a minicourse at NCGOA 13, Vanderbilt
University, May, 2013, on "Variants of Ktheory and connections
with noncommutative geometry and physics".
 (with Charles
Doran and Stefan MendezDiez) Tduality for orientifolds and twisted
KRtheory, Lett. Math. Phys.
104 (2014), 13331364, arXiv:1306.1779, doi: 10.1007/s1100501407150.
 (with Varghese
Mathai) Tduality for circle bundles via noncommutative geometry,
arXiv:1306.4198, Adv. Theor. Math. Phys. 18 (2014),
no. 6, 14371462, doi: 10.4310/ATMP.2014.v18.n6.a6.
 LeviCivita's
Theorem for noncommutative tori, SIGMA (Symmetry, Integrability and
Geometry: Methods and Applications) 9 (2013), 071, 9 pages, doi:
10.3842/SIGMA.2013.071.
See also this lecture on this material
from the Noncommutative Geometry Festival at TAMU in spring, 2014.
 (with Charles
Doran and Stefan MendezDiez) String theory on elliptic curve
orientifolds and KRtheory, arXiv:1402.4885, Comm. Math. Phys.
335 (2015), no. 2, 9551001. doi: 10.1007/s0022001422000.
 Real BaumConnes
assembly and Tduality for torus orientifolds, J. Geom. and Phys.
89 (2015), 2431, arXiv:1407.7735, doi:
10.1016/j.geomphys.2014.12.004
 Algebraic
Ktheory and derived equivalences
suggested by Tduality for torus orientifolds, J. Pure Appl. Algebra
221 (2017), no. 7, 17171728, arXiv:1604.04535.
 (with Mathai Varghese) Group dualities, Tdualities, and twisted Ktheory, J.
Lond. Math. Soc. 97 (2018), no. 1, 123, arXiv:1603.00969
 (with Patrick Chao) Different definitions of conic sections in hyperbolic geometry, Involve
11 (2018), no. 5, 753768, arXiv:1603.09285
 A new
approach to twisted Ktheory of compact Lie groups, arXiv:1708.05541. To appear in Alg. Geom. Top.
 (with Boris Botvinnik) Positive
scalar curvature on manifolds with fibered singularities,
arXiv:1808.06007
 (with David Wraith) Positive Scalar
Curvature and Applications, Snapshots of modern mathematics from
Oberwolfach (2019), no. 4
 (with Mathai Varghese) The RiemannRoch Theorem on
higher dimensional complex noncommutative tori, arXiv:1907.10200