Jonathan M. Rosenberg
Primary research areas:
Representation theory of Lie groups, C*-algebras,
K-theory, 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:
Some recent publications:
- (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), 379-381.
(For the Brown-Guivarc'h paper itself,
C*-algebras of some real and p-adic solvable groups,
Pacific J. Math. 65 (1976), no. 1, 175-192.
- Frobenius reciprocity for square-integrable
Illinois Journal of Mathematics 21 (1977), no. 4, 818-825.
Quick Proof of Harish-Chandra's Plancherel Theorem for Spherical
Functions on a Semisimple Lie Group, Proc. Amer. Math. Soc. 63
on random walks on semi simple Lie groups,
Mémoires de la Société Mathématique
de France 54 (1977), 119-127.
of crossed products of C*-algebras, Comm. Math. Phys. 57 (1977), no. 2, 187-191.
- (with Edward Effros)
C*-algebras with approximately inner flip, Pacific J. Math. 77 (1978), no. 2, 417--443.
Factor Representations of Locally Compact Groups,
Trans. Amer. Math. Soc. 237 (1978), 1-33.
to "Crossed products of UHF algebras by
product type actions" by Ola Bratteli, Duke Math. J. 46 (1979), no. 1,
- (with E. Gootman) The structure of crossed product C*-algebras:
a proof of the generalized Effros-Hahn conjecture,
Invent. Math. 52 (1979), no. 3, 283--298.
of Square-Integrable Representations of Unimodular Lie Groups on
Trans. Amer. Math. Soc. 261 (1980), 1-32.
- (with Claude Schochet) The classification of extensions of C*-algebras,
Bull. Amer. Math. Soc. (N.S.) 4 (1981), no. 1, 105-110.
- (with Claude Schochet)
functors classifying extensions of C*-algebras, J. Operator Theory 5 (1981),
no. 2, 267-282.
- (with Richard Herman)
group actions on C*-algebras, J. Operator Theory 6 (1981), no. 1,
The role of K-theory in noncommutative algebraic
topology, in Operator algebras and K-theory (San Francisco,
Calif., 1981), pp. 155-182, Contemp. Math., 10, Amer. Math. Soc., Providence,
positive scalar curvature, and the Novikov
conjecture, Publ. Math. IHES 58 (1983), 197-212.
- C*-algebras, positive scalar
curvature and the Novikov conjecture. II in
Geometric methods in operator algebras (Kyoto, 1983), 341--374,
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), 95-115,
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. 301-330.
- (with Steven Hurder, Dorte Olesen, and Iain Raeburn)
The Connes spectrum for actions of
abelian groups on continuous-trace algebras,
Ergodic Thy. and Dyn. Systems 6 (1986), no. 4, 541-560.
- C*-algebras, positive scalar curvature,
and the Novikov conjecture, III, Topology 25, no. 3 (1986), 319-336.
- (with Claude Schochet) The
Künneth theorem and the universal coefficient theorem
for Kasparov's generalized K-functor,
Duke Math. J. 55, no. 2 (1987), 431-474.
- (with Claude Schochet)
The Künneth Theorem and the Universal Coefficient Theorem for
Equivariant K-Theory and KK-Theory, 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), 15-18.
- Applications of analysis on Lipschitz manifolds, Miniconferences on harmonic analysis and operator algebras,
Proc. Centre for Mathematical Analysis, Austral. Nat. Univ., vol. 16,
- (with Iain Raeburn) Crossed
Products of Continuous-Trace C*-Algebras by Smooth Actions,
Trans. Amer. Math. Soc. 305 (1988), 1-45.
- Continuous-Trace -Algebras
from the Bundle Theoretic Point of View,
J. Australian Math. Soc. (Ser. A) 47 (1989), 368-381.
- (with Roger Howe) The unitary
representation theory of GL(n) of an infinite discrete field,
Israel J. Math. 67 (1989), no. 1, 67-81.
- (with Shmuel Weinberger) An equivariant
Novikov conjecture, With an appendix by J. P. May, K-Theory
4 (1990), no. 1, 29-53.
- The KO-assembly map
and positive scalar curvature, in
Algebraic topology, Poznan, 1989, 170-182,
Lecture Notes in Math., 1474, Springer, Berlin, 1991.
- (with Shmuel Weinberger) Higher G-signatures
for Lipschitz manifolds, K-Theory 7 (1993), 101-132.
- C*-algebras and Mackey's theory of
group representations (in "C*-algebras: 1943-1993 [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), 17-52.
- (with Shmuel Weinberger) Higher
G-indices and applications, Annales Scientifiques de
l'École Normale Supérieure (4) 21 (1998), 479-495.
theory, an article from the Encyclopaedia of Mathematics
- "Algebraic K-Theory and its Applications," Graduate Texts in
Mathematics, vol. 147,
Springer-Verlag, New York,
1994 (approx. 400 pages). ISBN 0-387-94248-3.
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," co-edited
with Steve Ferry and Andrew Ranicki, London Math. Soc. Lecture Notes,
vols. 226 and 227 (approx. 380 pages each),
Cambridge Univ. Press,
1995. ISBN 0-521-49796-5 and ISBN 0-521-49795-7. Some
errata are available.
- (with Stephan Stolz),
"A "stable" version of the Gromov-Lawson conjecture," in "The Čech Centennial: A Conference on Homotopy Theory," M. Cenkl
and H. Miller, eds., Contemp. Math., vol. 181, Amer. Math. Soc., 1995,
- (with Ronald L. Lipsman),
"The behavior of Fourier transforms on nilpotent
Lie groups," Trans. Amer. Math. Soc. 384 (1996), 1031-1050.
- "Lajos Pukánszky: In memorium,"
Notices Amer. Math. Soc. 45 (1998), 492. The whole
collection of memorial articles in this issue of the Notices is
- "The algebraic K-theory of operator
algebras." Appeared in K-Theory 12 (1997), 75-99.
The dvi file uses the xypic-fonts. 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 K-theory 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.
404-415. 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 K-Theory at Seattle in July,
1997. A more complete version
that appeared in the
proceedings of the conference, PSPUM/67, AMS, 1999, pp. 231-248,
is also available.
- "The K-homology class of the
Euler characteristic operator is trivial,"
Proc. Amer. Math. Soc.
127 (1999), pp. 3467-3474.
- (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 K-homology 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 G-Signature Theorem
Revisited." Appeared in
Aviv Topology Conference: Rothenberg
Festschrift, M. Farber, W. Lück, and S. Weinberger, eds.,
Contemp. Math. 231, Amer. Math. Soc., 1999, pp. 251-264.
The paper is also
available in pdf format (approx. 280kb).
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
non-commutative geometry to topology, slides for lectures at the
Symposium and AMS
Summer Research Conference
on Noncommutative Geometry at Mount Holyoke
College, June, 2000. (pdf format, approx 900kb)
- A history of non-commutative
harmonic analysis in 20th century Hungarian mathematics, for
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",
- The Yamabe invariant for non-simply
connected manifolds, with Boris Botvinnik,
Differential Geometry 62 (2002), no. 2, 175-208.
(pdf format, approx 280kb)
- Groupoid C*-algebras and index theory on
manifolds with singularities (PDF format, approx 220kb),
Dedicata 100 (2003), no. 1, 65-84.
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
Conference in honor of Blaine Lawson, June, 2002, on "Recent progress on
the Gromov-Lawson 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, 545--556.
Also available as a
- The equivariant Lefschetz fixed point theorem
for proper cocompact G-manifolds (pdf format, approx 300kb),
with Wolfgang Lück, Proc. Trieste Conf. on High-Dimensional
Manifolds, 2001, T. Farrell, L. Göttsche, and W. Lück, eds.,
World Scientific, 2003.
- Equivariant Euler characteristics and
K-homology Euler classes for proper cocompact G-manifolds
(pdf format, approx 380kb),
with Wolfgang Lück, Geometry and
Topology 7 (2003), 569-613.
Also available in postscript format.
- Slides for a talk on "A selective
history of the Stone-von 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
- K-theory and geometric topology,
a survey article from the "Handbook of Algebraic
K-theory", edited by Eric Friedlander and Dan Grayson,
Springer, 2004, pp. 577-610. Published version
now available online.
- A Selective History of the
Stone-von Neumann Theorem (pdf format, approx 340kb), in
Operator algebras, quantization, and noncommutative geometry,
Contemp. Math., 365, Amer. Math. Soc., Providence, RI, 2004, pp. 123-158.
for torus bundles via noncommutative topology, with Varghese Mathai,
Comm. Math. Physics 253 (2005), no. 3, 705-721.
- The signature operator
at 2, with Shmuel Weinberger, Topology
45 (2006), no. 1, 47-63.
- Comparison Between Algebraic and
Topological K-Theory for Banach Algebras and
C*-Algebras, a survey article from the "Handbook
of Algebraic K-theory", edited by Eric Friedlander and Dan Grayson,
Springer, 2004, pp. 843-874. Published version
now available online.
- A K-theory perspective
on T-duality in string theory, slides for a talk at the
K-theory Conference, X. This talk is based on the
material of #32 above.
- On mysteriously missing T-duals,
H-flux and the T-duality group, with Varghese Mathai,
to appear in "Proceedings of the XXXIII International
Conference of Differential Geometric Methods in Mathematical Physics"
(August 2005), editors Mo-Lin Ge and Weiping Zhang,
World Scientific 2006.
- Slides and
homework exercises from the
Seminar on Topological K-Theory of Noncommutative
Algebras and Applications.
- T-duality for torus bundles with
H-fluxes via noncommutative topology, II: the high-dimensional case
and the T-duality group, with Varghese Mathai,
Advances in Theoretical and Mathematical Physics 10 (2006),
no. 1, 123-158.
- An analogue of the Novikov Conjecture
in complex algebraic geometry, Trans. Amer. Math. Soc.
360 (2008), no. 1, 383-394.
- A review of The Novikov Conjecture:
Geometry and Algebra, by Matthias Kreck and Wolfang Lück,
Bull. Amer. Math. Soc. 43 (2006), 599-604.
- D-branes, RR-fields and Duality on
Noncommutative Manifolds, with Jacek Brodzki, Varghese Mathai, and
Richard J. Szabo, Comm. Math. Physics 277 (2008),
no. 3, 643-706.
- 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 (UTF-16) if you want the Hebrew to
- Notes from a talk at Oberwolfach on
- 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".
variations on Laplace's equation, based in part on #45 above,
in Analysis and PDE, 1
(2008), no. 1, 95-114, arXiv:0802.4033.
Noncommutative correspondences, duality and D-branes in bivariant K-theory,
with Jacek Brodzki, Varghese Mathai, and Richard J. Szabo,
Adv. in Theoretical and
Math. Phys. 13 (2009), no. 2, 497-552,
- 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. 1-2,
- A noncommutative sigma-model,
with Varghese Mathai, J.
of Noncommutative Geometry 5 (2011), no. 2, 265-294.
- Notes and slides from course at
the Buenos Aires Winter School on Noncommutative Geometry, July-August
2010, to appear in Clay Math. Proc. 16 (2012), 93-129.
- Introduction to Proc. Symp. Pure Math., vol. 81,
"Superstrings, geometry, topology, and C*-algebras", Amer. Math. Soc., 2010.
- (with Stefan
Mendez-Diez) K-theoretic matching of brane charges in S- and
U-duality, arxiv:1007.1202, Adv. Theor. Math. Phys.
16 (2012), no. 6, 1591-1618.
- Slides from a lecture series at RIMS,
Kyoto, February, 2011, on Dualities in field theories and
the role of K-theory.
- Dualities in
field theories and the role of K-theory, arxiv:1107.5015,
Noncommutative Geometry and Physics, 3, ed. by Giuseppe Dito
et al., World Scientific, 2013, 485-506.
- Some work of Stefan Banach and
the mathematics it has generated,
Wiadomości Matematyczne 48 (2012),
no. 2, 217-212. (Special issue about Polish mathematicians for the
6th European Congress of Mathematics, 2012.)
Künneth Theorem in equivariant K-theory for actions of a cyclic
group of order 2, Alg. and
Geom. Topology 13 (2013) 1225-1241, arXiv:1208.6355.
Yehoshua Dan Agassi) Flux quantization for a superconducting ring in
the shape of a Möbius band, arXiv:1301.2743.
for a minicourse at NCGOA 13, Vanderbilt
University, May, 2013, on "Variants of K-theory and connections
with noncommutative geometry and physics".
- (with Charles
Doran and Stefan Mendez-Diez) T-duality for orientifolds and twisted
KR-theory, Lett. Math. Phys.
104 (2014), 1333-1364, arXiv:1306.1779, doi: 10.1007/s11005-014-0715-0.
- (with Varghese
Mathai) T-duality for circle bundles via noncommutative geometry,
arXiv:1306.4198, Adv. Theor. Math. Phys. 18 (2014),
no. 6, 1437-1462, doi: 10.4310/ATMP.2014.v18.n6.a6.
Theorem for noncommutative tori, SIGMA (Symmetry, Integrability and
Geometry: Methods and Applications) 9 (2013), 071, 9 pages, doi:
See also this lecture on this material
from the Noncommutative Geometry Festival at TAMU in spring, 2014.
- (with Charles
Doran and Stefan Mendez-Diez) String theory on elliptic curve
orientifolds and KR-theory, arXiv:1402.4885, Comm. Math. Phys.
335 (2015), no. 2, 955-1001. doi: 10.1007/s00220-014-2200-0.
- Real Baum-Connes
assembly and T-duality for torus orientifolds, J. Geom. and Phys.
89 (2015), 24-31, arXiv:1407.7735, doi:
K-theory and derived equivalences
suggested by T-duality for torus orientifolds, J. Pure Appl. Algebra
221 (2017), no. 7, 1717-1728, arXiv:1604.04535.
- (with Mathai Varghese) Group dualities, T-dualities, and twisted K-theory, J.
Lond. Math. Soc. 97 (2018), no. 1, 1-23, arXiv:1603.00969
- (with Patrick Chao) Different definitions of conic sections in hyperbolic geometry, Involve
11 (2018), no. 5, 753-768, arXiv:1603.09285
- A new
approach to twisted K-theory of compact Lie groups, arXiv:1708.05541. To appear in Alg. Geom. Top.
- (with Boris Botvinnik) Positive
scalar curvature on manifolds with fibered singularities,
- (with David Wraith) Positive Scalar
Curvature and Applications, Snapshots of modern mathematics from
Oberwolfach (2019), no. 4
- (with Mathai Varghese) The Riemann-Roch Theorem on
higher dimensional complex noncommutative tori, arXiv:1907.10200