Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
|
   
Mobile Device Pairing
Journal of the American Mathematical Society
Journal of the American Mathematical Society
ISSN 1088-6834(e) ISSN 0894-0347(p)

     

Analytic torsion and $             R$-torsion for unimodular representations

Author(s): Werner Müller
Journal: J. Amer. Math. Soc. 6 (1993), 721-753.
MSC: Primary 58G26; Secondary 57Q10, 58G11
MathSciNet review: 1189689
Retrieve article in: PDF
This article is available free of charge

References | Similar articles | Additional information

References:

[B-NW]
D. Bar-Natan and E. Witten, Perturbative expansion of Chern-Simons theory with noncompact gauge group, preprint, IASSNS-HEP-91/4, Princeton, 1991. MR 1133274 (93c:81244)

[B-Z]
J.-M. Bismut and W. Zhang, An extension of a theorem by Cheeger and Müller, Astérisque 205 (1992). MR 1185803 (93j:58138)

[BW]
A. Borel and N. Wallach, Continuous cohomology, discrete subgroups, and representations of reductive groups, Ann. of Math. Stud., vol. 94, Princeton Univ. Press, Princeton, NJ, 1980. MR 554917 (83c:22018)

[C]
J. Cheeger, Analytic torsion and the heat equation, Ann. of Math. (2) 109 (1979), 259-322. MR 528965 (80j:58065a)

[FG]
D. S. Freed and R. E. Gompf, Computer calculations of Witten's $ 3$-manifold invariant, Comm. Math. Phys. 141 (1991), 79-117. MR 1133261 (93d:57027)

[K]
T. P. Killingback, Quantization of $ {\text{SL}}(2,{\mathbf{R}})$ Chern-Simons theory, Comm. Math. Phys. 145 (1992), 1-16. MR 1155281 (93f:58090)

[MM]
Y. Matsushima and S. Murakami, On vector bundle valued harmonic forms and automorphic forms on symmetric spaces, Ann. of Math. (2) 78 (1963), 365-416. MR 0153028 (27:2997)

[Mi1]
J. Milnor, Whitehead torsion, Bull. Amer. Math. Soc. 72 (1966), 358-426. MR 0196736 (33:4922)

[Mi2]
-, A duality theorem for Reidemeister torsion, Ann. of Math. (2) 76 (1962), 137-147. MR 0141115 (25:4526)

[MS]
H. Moscovici and R. J. Stanton, $             R$-torsion and zeta functions for locally symmetric manifolds, Invent. Math. 105 (1991), 185-216. MR 1109626 (92i:58199)

[Mü]
W. Müller, Analytic torsion and $ R$-torsion of Riemannian manifolds, Adv. in Math. 28 (1978), 233-305. MR 498252 (80j:58065b)

[Mu]
J. Munkres, Elementary differential topology, Ann. of Math. Stud., vol. 54, Princeton Univ. Press, Princeton, NJ, 1961. MR 0163320 (29:623)

[R]
M. S. Raghunathan, On the first cohomology of discrete subgroups of semi-simple Lie groups, Amer. J. Math. 87 (1965), 103-139. MR 0173730 (30:3940)

[RS]
D. B. Ray and I. M. Singer, $ R$-torsion and the Laplacian on Riemannian manifolds, Adv. in Math. 7 (1971), 145-210. MR 0295381 (45:4447)

[RT]
N. Yu. Reshetikhin and V. G. Turaev, Invariants of $ 3$-manifolds via link polynomials and quantum groups, Invent. Math. 103 (1991), 547-597. MR 1091619 (92b:57024)

[S]
A. Schwarz, The partition function of degenerate quadratic functional and Ray-Singer invariants, Lett. Math. Phys. 2 (1978), 247-252. MR 0676337 (58:32690)

[Se]
R. T. Seeley, Complex powers of an elliptic operator, Proc. Sympos. Pure Math., vol. 10, Amer. Math. Soc., Providence, RI, 1967, pp. 288-315. MR 0237943 (38:6220)

[Wa]
G. Warner, Harmonic analysis on semi-simple Lie groups. I, Springer-Verlag, Berlin, Heidelberg, and New York, 1972. MR 0498999 (58:16979)

[W1]
E. Witten, Quantum field theory and the Jones polynomial, Comm. Math. Phys. 121 (1988), 351-399. MR 990772 (90h:57009)

[W2]
E. Witten, 2 + 1 dimensional gravity as an exactly soluble system, Nuclear Phys. B 311 (1988/89), 46-78. MR 974271 (90a:83041)

[W3]
E. Witten, Quantization of Chern-Simons gauge theory with complex gauge group, Comm. Math. Phys. 137 (1991), 29-66. MR 1099255 (92f:58072)

Similar Articles:

Retrieve articles in Journal of the American Mathematical Society with MSC: 58G26, 57Q10, 58G11

Retrieve articles in all Journals with MSC: 58G26, 57Q10, 58G11


Additional Information:

DOI: 10.1090/S0894-0347-1993-1189689-4
PII: S0894-0347-1993-1189689-4
Copyright of article: Copyright 1993, American Mathematical Society




AMS and Social Media LinkedIn Facebook Podcasts Twitter YouTube RSS Feeds Blogs Wikipedia