|
-invariants and their adiabatic limits
Author(s):
Jean-Michel
Bismut;
Jeff
Cheeger
Journal:
J. Amer. Math. Soc.
2
(1989),
33-70.
MSC:
Primary 58G10;
Secondary 58C50, 58G12, 58G20
MathSciNet review:
966608
Retrieve article in:
PDF
This article is available free of charge
References |
Similar articles |
Additional information
References:
-
- [A]
- M. F. Atiyah, The logarithm of the Dedekind
-function, Math. Ann. 278 (1987), 335-380. MR 909232 (89h:58177) - [ADS]
- M. F. Atiyah, H. Donnelly, and I. M. Singer, Eta invariants, signature defects of cusps, and values of
-functions, Ann. of Math. (2) 118 (1983), 131-177. MR 707164 (86g:58134a) - [APS]
- M. F. Atiyah, V. K. Patodi, and I. M. Singer, Spectral asymmetry and Riemannian geometry, I, Math. Proc. Cambridge Philos. Soc. 77 (1975), 43-69. MR 0397797 (53:1655a)
- [AS]
- M. F. Atiyah and I. M. Singer, Dirac operators coupled to vector potentials, Proc. Nat. Acad. Sci. U.S.A. 81 (1984), 2597. MR 742394 (86g:58127)
- [BaM]
- D. Barbasch and H. Moscovici,
-index theorem and the Selbert trace formula, J. Funct. Anal. 53 (1983), 151-201. MR 722507 (85j:58137) - [B1]
- J.-M. Bismut, The Atiyah-Singer Index Theorem for families of Dirac operators: two heat equation proofs, Invent. Math. 83 (1986), 91-151. MR 813584 (87g:58117)
- [B2]
- -, Transgressed Chern forms for Dirac operators, J. Funct. Anal. 77 (1988), 32-50. MR 930389 (89j:58123)
- [BC1]
- J. M. Bismut and J. Cheeger, Invariants êta et indice des familles pour des varietes a bord, C. R. Acad. Sci. Paris Sér I. 305 (1987), 127-130. MR 901625 (88g:58171)
- [BC2]
- -, Families index for manifolds with boundary, superconnections and cones, J. Funct. Anal. (to appear).
- [BF]
- J. M. Bismut and D. S. Freed, The analysis of elliptic families: Dirac operators, eta invariants, and the holonomy theorem of Witten, Comm. Math. Phys. 107 (1986), 103-163. MR 861886 (88h:58110b)
- [BGS]
- J. M. Bismut, H. Gillet, and C. Soulé, Analytic torsion and holomorphic determinant bundles, II; Direct images and Bott-Chern forms, Comm. Math. Phys. 115 (1988), 79-126. MR 929147 (89g:58192b)
- [C1]
- J. Cheeger, On the spectral geometry of spaces with cone-like singularities, Proc. Nat. Acad. Sci. USA, Vol. 76, No. 5, pp. 2103-2106, May 1979. MR 530173 (80k:58098)
- [C2]
- -, Spectral geometry of singular Riemannian spaces, J. Differential Geom. 18 (1983), 575-657. MR 730920 (85d:58083)
- [C3]
- -,
-invariants, the adiabatic approximation and conical singularities, J. Differential Geom. 26 (1987), 175-221. MR 892036 (89c:58123) - [Chou]
- A. Chou, The Dirac operator on spaces with conical singularities and positive scalar curvature, Trans. Amer. Math. Soc. 28 (1985), 1-40. MR 779050 (86i:58124)
- [Co]
- A. Connes, Noncommutative differential geometry, Inst. Haute Études Sci. Publ. Math. 62 (1986) 41-144. MR 823176 (87i:58162)
- [CoM]
- A. Connes and H. Moscovici, Transgression of the Chern character and cyclic cohomology, C. R. Acad. Sci. Paris Sér. I 303 (1986), 913-918. MR 873393 (88c:58006)
- [D]
- X. Dai, Ph.D. thesis, SUNY at Stony Brook (in preparation).
- [G]
- E. Getzler, A short proof of the Atiyah-Singer Index Theorem, Topology 25 (1986), 111-117. MR 836727 (87h:58207)
- [Gi1]
- P. Gilkey, Invariance theory, the heat equation, and the Atiyah-Singer index theorem, Math. Lecture Series., No. 11, Publish or Perish, Boston, 1984. MR 783634 (86j:58144)
- [M1]
- W. Müller, Signature defects of cusps of Hilbert modular varieties and values of
-series at , J. Differential Geometry 20 (1984), 55-119. MR 772126 (87c:11048) - [M2]
- -, Manifolds with cusps of rank one: spectral theory and
-index theorem, Lecture Notes in Math., no. 1244, Springer-Verlag, New York, 1987. MR 891654 (89g:58196) - [Q]
- D. Quillen, Superconnections and the Chern character, Topology 24 (1985), 89-95. MR 790678 (86m:58010)
- [S]
- M. Stern,
-index theorems on locally symmetric spaces (preprint). - [W]
- E. Witten, Global gravitational anomalies, Comm. Math. Phys. 100 (1985), 197-229. MR 804460 (87k:58282)
Similar Articles:
Retrieve articles in Journal of the American Mathematical Society
with
MSC:
58G10,
58C50, 58G12, 58G20
Retrieve articles in all Journals with
MSC:
58G10,
58C50, 58G12, 58G20
Additional Information:
DOI:
10.1090/S0894-0347-1989-0966608-3
PII:
S0894-0347-1989-0966608-3
Copyright of article:
Copyright
1989,
American Mathematical Society
|