Transgressed Euler classes of SL (2n,𝐙) vector bundles, adiabatic limits of eta invariants and special values of L-functions
Annales scientifiques de l'École Normale Supérieure, Série 4, Tome 25 (1992) no. 4, pp. 335-391. 
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     author = {Bismut, Jean-Michel and Cheeger, Jeff},
     title = {Transgressed {Euler} classes of ${\rm SL}(2n,\mathbf {Z})$ vector bundles, adiabatic limits of eta invariants and special values of $L$-functions},
     journal = {Annales scientifiques de l'\'Ecole Normale Sup\'erieure},
     pages = {335--391},
     publisher = {Elsevier},
     volume = {Ser. 4, 25},
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     year = {1992},
     doi = {10.24033/asens.1653},
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     url = {http://archive.numdam.org/articles/10.24033/asens.1653/}
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Bismut, Jean-Michel; Cheeger, Jeff. Transgressed Euler classes of ${\rm SL}(2n,\mathbf {Z})$ vector bundles, adiabatic limits of eta invariants and special values of $L$-functions. Annales scientifiques de l'École Normale Supérieure, Série 4, Tome 25 (1992) no. 4, pp. 335-391. doi : 10.24033/asens.1653. http://archive.numdam.org/articles/10.24033/asens.1653/

[A] M. F. Atiyah, The Logarithm of the Dedekind η-Function, Math. Annal., Vol. 278, 1987, pp. 335-380. | MR | Zbl

[ABo] M. F. Atiyah and R. Bott, A Lefschetz Fixed Point Formula for Elliptic Complexes, Ann. Math. II, Vol. 88, 1968, pp. 451-491. | MR | Zbl

[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. | MR | Zbl

[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. | MR | Zbl

[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. | MR | Zbl

[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. | MR | Zbl

[AS] M. F. Atiyah and I. M. Singer, The Index of Elliptic Operator IV, Ann. Math., Vol. 93, 1971, pp. 119-138. | MR | Zbl

[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. | MR | Zbl

[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. | MR | Zbl

[BC] J. M. Bismut and J. Cheeger, η-Invariants and their Adiabatic Limits, J. A.M.S., Vol. 2, 1989, pp. 33-70. | MR | Zbl

[BF] J. M. Bismut and D. S. Freed, The Analysis of Elliptic Families II, Comm. Math. Phys., Vol. 107, 1986, pp. 103-163. | MR | Zbl

[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. | MR | Zbl

[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. | MR | Zbl

[CaSha] S. Cappell and J. Shaneson, Piecewise Linear Embeddings, Ann. Math., Vol. 103, 1976, pp. 163-228. | MR | Zbl

[C] J. Cheeger, η-Invariants, the Adiabatic Approximation and Conical Singularities, J. Diff. Geom., Vol. 26, 1987, pp. 175-221. | MR | Zbl

[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. | MR | Zbl

[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. | MR | Zbl

[Ch] S. S. Chern, A Simple Intrinsic Proof of the Gauss-Bonnet Formula for Closed Manifolds, Ann. Math., Vol. 45, 1944, pp. 747-752. | MR | Zbl

[D] X. Dai, Ph. D thesis, SUNY, 1989.

[H] F. Hirzebruch, Hilbert Modular Surfaces. Enseign. Math., 1973, pp. 183-281. | MR | Zbl

[LeSc] R. Lee and R. Sczarba, On the Torsion of K4 (ℤ) and K5 (ℤ), Duke Math. J., Vol. 45, 1978, pp. 101-129. | Zbl

[L] A. Lichnerowicz, Spineurs harmoniques, C. R. Acad. Sci. Paris, T. 257, Série A, 1963, pp. 7-9. | MR | Zbl

[Ma] Y. Manin, Gauge Field Theory and Complex Geometry, Grundl. der Math. Wiss, Vol. 289, Berlin-Heidelberg-New York, Springer, 1988. | MR | Zbl

[MQ] V. Mathai and D. Quillen, Superconnections, Thom Classes and Equivariant Differential Forms, Topology, 25, 1986, pp. 85-110. | MR | Zbl

[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. | MR | Zbl

[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. | Zbl

[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. | Zbl

[Q] D. Quillen, Superconnections and the Chern Character, Topology, Vol. 24, 1985, pp. 89-95. | MR | Zbl

[Sa] F. Sato Zeta Functions in Several Variables Associated with Prehomogeneous Vector Spaces. I. Functional Equations, Tôhoku Math. J., Vol. 34, 1982, pp. 437-483. | MR | Zbl

[Sat Shin] M. Sato and T. Shintani, On Zeta Functions Associated with Prehomogeneous Vector Spaces, Ana. Math., Vol. 100, 1974, pp. 131-170. | MR | Zbl

[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. | MR | Zbl

[Su2] D. Sullivan, Geometric Topology Seminar Notes, Princeton University, 1967.

[Su3] D. Sullivan, Geometric Topology, Part I, M.I.T., 1970.

[Sh] H. Shimizu, On Discontinuous Groups Acting on the Product of Upper Half Planes, Ann. Math., Vol. 77, 1963, pp. 33-71. | MR | Zbl

[Si] C. L. Siegel, Uber die Fourierschen Koeffizienten von Modulformen. Göttingen Nachrichten, Math. Phys. Classe, 1970, pp. 15-56. | MR | Zbl

[St] M. Stern, Lefschetz formulae for arithmetic varieties (preprint).

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