Transgressed Euler classes of $\mathrm{SL}(2n,𝐙)$ vector bundles, adiabatic limits of eta invariants and special values of $L$-functions

 Access to full text

 Full (PDF)

1. [A] M. F. ATIYAH, The Logarithm of the Dedekind η-Function, Math. Annal., Vol. 278, 1987, pp. 335-380. Zbl0648.58035MR89h:58177
2. [ABo] M. F. ATIYAH and R. BOTT, A Lefschetz Fixed Point Formula for Elliptic Complexes, Ann. Math. II, Vol. 88, 1968, pp. 451-491. Zbl0167.21703MR38 #731
3. [ABoP] M. F. ATIYAH, R. BOTT and V. K. PATODI, On the Heat Equation and the Index Theorem, Invent. Math., Vol. 19, 1973, pp. 279-330. Zbl0257.58008MR58 #31287
4. [ADS] M. F. ATIYAH, H. DONNELLY and I. M. SINGER, Eta Invariants, Signature Defects of Cusps and Values of L-Functions, Ann. Math., Vol. 18, 1983, pp. 131-177. Zbl0531.58048MR86g:58134a
5. [APS1] M. F. ATIYAH, V. K. PATODI and I. M. SINGER, Spectral Asymmetry and Riemannian Geometry. I, Math. Proc. Cambridge Philos. Soc., Vol. 77, 1975, pp. 43-69. Zbl0297.58008MR53 #1655a
6. [APS2] M. F. ATIYAH, V. K. PATODI and I. M. SINGER, Spectral Asymmetry and Riemannian Geometry. II, Math. Proc. Cambridge Philos. Soc., Vol. 78, 1976, pp. 405-432. Zbl0314.58016MR53 #1655b
7. [AS] M. F. ATIYAH and I. M. SINGER, The Index of Elliptic Operator IV, Ann. Math., Vol. 93, 1971, pp. 119-138. Zbl0212.28603MR43 #5554
8. [B1] J. M. BISMUT, The Atiyah-Singer Index Theorem for Families of Dirac Operators : Two Heat Equation Proofs, Invent. Math., Vol. 83, 1986, pp. 91-151. Zbl0592.58047MR87g:58117
9. [B2] J. M. BISMUT, Formules de Lichnerowicz et théorème de l'indice, in Géométrie différentielle, D. BERNARD, Y. CHOQUET-BRUHAT Ed., pp. 11-31. Travaux en cours, Paris, Hermann, 1988. Zbl0648.58033MR90f:58165
10. [BC] J. M. BISMUT and J. CHEEGER, η-Invariants and their Adiabatic Limits, J. A.M.S., Vol. 2, 1989, pp. 33-70. Zbl0671.58037MR89k:58269
11. [BF] J. M. BISMUT and D. S. FREED, The Analysis of Elliptic Families II, Comm. Math. Phys., Vol. 107, 1986, pp. 103-163. Zbl0657.58038MR88h:58110b
12. [BGS1] J. M. BISMUT, H. GILLET and C. SOULÉ, Analytic Torsion and Holomorphic Determinant Bundles. II, Comm. Math. Phys., Vol. 115, 1988, pp. 79-126. Zbl0651.32017MR89g:58192b
13. [BGS2] J. M. BISMUT, H. GILLET and C. SOULÉ, Complex Immersions and Arakelov Geometry in The Grothendieck Festschrift, Vol. 1, P. CARTIER et al. Eds., pp. 249-331. Boston, Birkhaüser, 1990. Zbl0744.14015MR92a:14019
14. [CaSha] S. CAPPELL and J. SHANESON, Piecewise Linear Embeddings, Ann. Math., Vol. 103, 1976, pp. 163-228. Zbl0346.57005MR53 #11629
15. [C] J. CHEEGER, η-Invariants, the Adiabatic Approximation and Conical Singularities, J. Diff. Geom., Vol. 26, 1987, pp. 175-221. Zbl0623.58021MR89c:58123
16. [CGT] J. CHEEGER, M. GROMOV and M. TAYLOR, Finite Propagation Speed, Kernel Estimates of the Laplace Operator, and the Geometry of Complete Riemannian Manifolds, J. Diff. Geom., Vol. 17, 1982, pp. 15-53. Zbl0493.53035MR84b:58109
17. [CS] J. CHEEGER and J. SIMONS, Differential Characters and Geometric Invariants, in Geometry and Topology, J. ALEXANDER and J. HARER Ed., Lect. Notes Math., n° 1167, pp. 50-80, Berlin-Heidelberg-New York, Springer, 1985. Zbl0621.57010MR87g:53059
18. [Ch] S. S. CHERN, A Simple Intrinsic Proof of the Gauss-Bonnet Formula for Closed Manifolds, Ann. Math., Vol. 45, 1944, pp. 747-752. Zbl0060.38103MR6,106a
19. [D] X. DAI, Ph. D thesis, SUNY, 1989. 
20. [H] F. HIRZEBRUCH, Hilbert Modular Surfaces. Enseign. Math., 1973, pp. 183-281. Zbl0285.14007MR52 #13856
21. [LeSc] R. LEE and R. SCZARBA, On the Torsion of K4 (ℤ) and K5 (ℤ), Duke Math. J., Vol. 45, 1978, pp. 101-129. Zbl0385.18009
22. [L] A. LICHNEROWICZ, Spineurs harmoniques, C. R. Acad. Sci. Paris, T. 257, Série A, 1963, pp. 7-9. Zbl0136.18401MR27 #6218
23. [Ma] Y. MANIN, Gauge Field Theory and Complex Geometry, Grundl. der Math. Wiss, Vol. 289, Berlin-Heidelberg-New York, Springer, 1988. Zbl0641.53001MR89d:32001
24. [MQ] V. MATHAI and D. QUILLEN, Superconnections, Thom Classes and Equivariant Differential Forms, Topology, 25, 1986, pp. 85-110. Zbl0592.55015MR87k:58006
25. [Mü1] W. MÜLLER, Signature Defects of Cusps of Hilbert Modular Varieties and Values of L Series at s = 1, J. Diff. Geom., Vol. 20, 1984, pp. 55-119. Zbl0575.10023MR87c:11048
26. [Mü2] W. MÜLLER, Manifolds with Cusps of Rank One : Spectral Theory and L2 Index Theorem, Lect. Notes Math., n° 1244, Berlin-Heidelberg-New York, Springer, 1987. Zbl0632.58001
27. [Mü3] W. MÜLLER, L2 Index Theory, Eta Invariants and Values of L-Functions, in Geometric and Topological Invariants of Elliptic Operators, J. KAMINKER Ed., pp. 145-189, Contemporary Math., n° 105, Providence, AMS, 1990. Zbl0705.58048
28. [Q] D. QUILLEN, Superconnections and the Chern Character, Topology, Vol. 24, 1985, pp. 89-95. Zbl0569.58030MR86m:58010
29. [Sa] F. SATOZeta Functions in Several Variables Associated with Prehomogeneous Vector Spaces. I. Functional Equations, Tôhoku Math. J., Vol. 34, 1982, pp. 437-483. Zbl0497.14007MR84e:12015a
30. [Sat Shin] M. SATO and T. SHINTANI, On Zeta Functions Associated with Prehomogeneous Vector Spaces, Ana. Math., Vol. 100, 1974, pp. 131-170. Zbl0309.10014MR49 #8969
31. [Su1] D. SULLIVAN, La classe d'Euler réelle d'un fibré vectoriel à groupe structural SLn (Z) est nulle, C. R. Acad. Sci. Paris, 281, Série A, 1975, pp. 17-18. Zbl0312.55022MR51 #9077
32. [Su2] D. SULLIVAN, Geometric Topology Seminar Notes, Princeton University, 1967. 
33. [Su3] D. SULLIVAN, Geometric Topology, Part I, M.I.T., 1970. 
34. [Sh] H. SHIMIZU, On Discontinuous Groups Acting on the Product of Upper Half Planes, Ann. Math., Vol. 77, 1963, pp. 33-71. Zbl0218.10045MR26 #2641
35. [Si] C. L. SIEGEL, Uber die Fourierschen Koeffizienten von Modulformen. Göttingen Nachrichten, Math. Phys. Classe, 1970, pp. 15-56. Zbl0225.10031MR44 #2706
36. [St] M. STERN, Lefschetz formulae for arithmetic varieties (preprint). 

1. Werner Müller, The eta invariant (some recent developments)
2. Weiping Zhang, Circle bundles, adiabatic limits of $\eta$-invariants and Rokhlin congruences