@incollection{SB_1993-1994__36__335_0, author = {M\"uller, Werner}, title = {The eta invariant (some recent developments)}, booktitle = {S\'eminaire Bourbaki : volume 1993/94, expos\'es 775-789}, series = {Ast\'erisque}, note = {talk:787}, pages = {335--364}, publisher = {Soci\'et\'e math\'ematique de France}, number = {227}, year = {1995}, mrnumber = {1321653}, zbl = {0842.58069}, language = {en}, url = {http://www.numdam.org/item/SB_1993-1994__36__335_0/} }
TY - CHAP AU - Müller, Werner TI - The eta invariant (some recent developments) BT - Séminaire Bourbaki : volume 1993/94, exposés 775-789 AU - Collectif T3 - Astérisque N1 - talk:787 PY - 1995 SP - 335 EP - 364 IS - 227 PB - Société mathématique de France UR - http://www.numdam.org/item/SB_1993-1994__36__335_0/ LA - en ID - SB_1993-1994__36__335_0 ER -
%0 Book Section %A Müller, Werner %T The eta invariant (some recent developments) %B Séminaire Bourbaki : volume 1993/94, exposés 775-789 %A Collectif %S Astérisque %Z talk:787 %D 1995 %P 335-364 %N 227 %I Société mathématique de France %U http://www.numdam.org/item/SB_1993-1994__36__335_0/ %G en %F SB_1993-1994__36__335_0
Müller, Werner. The eta invariant (some recent developments), in Séminaire Bourbaki : volume 1993/94, exposés 775-789, Astérisque, no. 227 (1995), Talk no. 787, 30 p. http://www.numdam.org/item/SB_1993-1994__36__335_0/
[Ar] Characters, harmonic analysis, and an -Lefschetz formula, Proc. Sympos. Pure Math., Vol. 48, Amer. Math. Soc., Providence, R.I. (1987), 167-179. | DOI | MR | Zbl
-[At] The logarithm of the Dedekind -function, Math. Annalen 278, 335-380 (1987). | DOI | EuDML | Zbl
-[APS1] Spectral asymmetry and Riemannian geometry, I, Math. Proc. Camb. Phil. Soc. 77, 43-69 (1975). | DOI | MR | Zbl
, , and -[APS2] Spectral asymmetry and Riemannian geometry, II, Math. Proc. Camb. Phil. Soc. 78, 405-432 (1975). | DOI | MR | Zbl
, , and -[APS3] Spectral asymmetry and Riemannian geometry, III, Math. Proc. Camb. Phil. Soc. 79, 71-99 (1976). | DOI | MR | Zbl
, , and -[AS] The index of elliptic operators, IV, Ann. of Math. 93, 119-138 (1971). | DOI | MR | Zbl
and -[Ba] Mathematical scattering theory, Akademie-Verlag, Berlin 1983. | DOI | MR | Zbl
and -[Bi] The Atiyah-singer index theorem for families of Dirac operators : Two heat equation proofs, Invent. math. 83, 91-151 (1986). | DOI | EuDML | MR | Zbl
-[BC1] Eta invariants and their adiabatic limits, J. Amer. Math. Soc. 2, 33-70 (1989). | MR | Zbl
and -[BC2] Transgressed Euler classes of vector bundles, adiabatic limits of eta invariants and special values of L-functions, Ann. scient. Ec. Norm. Sup., 4e série, t. 25, 335-391 (1992). | DOI | EuDML | Numdam | MR | Zbl
and -[BC3] Families index for manifolds with boundary, superconnections and cones, I, Journal Funct. Anal. 89, 313-363 (1990). | DOI | MR | Zbl
and -[BC4] Families index for manifolds with boundary, superconnections and cones, II, Journal Funct. Anal. 90, 306-354 (1990). | DOI | MR | Zbl
and -[BC5] Remarks on the index theorem for families of Dirac operators on manifolds with boundary, in: Differential Geometry, 59- 83, A symposium in honor of Manfredo do Carmo. ed. B. Lawson and K. Tenenblat, Longman Scientific & Technical, 1991. | MR | Zbl
and -[BF1] The analysis of elliptic families, I, Commun. Math. Phys. 106, 159-176 (1986). | MR | Zbl
and -[BF2] The analysis of elliptic families, II, 107, 103-163 (1986). | MR | Zbl
and -[Bo] Stable real cohomology of arithmetic groups, Ann. Sci. Éc. Norm. Super., 4e série, 7, 235-272 (1974). | DOI | EuDML | Numdam | MR | Zbl
-[BS] Corners and arithmetic groups, Comment. Math. Helv. 48, 244-297 (1974). | EuDML | MR | Zbl
and -[BMS] Relative index theorems and supersymmetric scattering theory, Commun. Math. Phys. 114, 475-513 (1988). | MR | Zbl
, and -[BG] Residues of the -function for operators of Dirac type, J. Funct. Anal. 108, 47-87 (1992). | Zbl
and -[Br1] -index theorems on certain complete manifolds, J. Diff. Geom. 32, 491-532 (1990). | MR | Zbl
-[Br2] On -index theorems for complete manifolds of rank-one type, Duke Math. J. 66, 257-309. | MR | Zbl
-[C1] On the spectral geometry of spaces with cone-like singularities, Proc. Nat. Acad. Sci. U.S.A. 76, 2103-2106 (1979). | MR | Zbl
-[C2] Spectral geometry of singular Riemannian spaces, J. Diff. Geom. 18, 575-657 (1983). | MR | Zbl
-[C3] -invariants, the adiabatic approximation and conical singularities, J. Diff. Geom. 26, 175-221 (1987). | Zbl
-[Da] Adiabatic limits, the non-multiplicativity of signature and Leray spectral sequence, J. Amer. Math. Soc. 4, 265-321 (1991). | MR | Zbl
-[DW] Adiabatic limits of the -invariants. The odd-dimensional Atiyah-Patodi-Singer problem, Commun. Math. Phys. 142, 139-168 (1991). | Zbl
and -[Gi1] The residue of the global eta function at the origin, Advances in Math. 40, 290-307 (1981). | MR | Zbl
-[Gi2] The boundary integrand in the formula for the signature and the Euler characteristic of a Riemannian manifold with boundary, Advances in Math. 15, 334-360 (1975). | MR | Zbl
-[GS] The eta invariant for a class of elliptic boundary value problems, Commun. Pure Appl. Math. 36, 85-132 (1983). | MR | Zbl
and -[GM] Topological trace formula (To appear). | MR
, -[He] Darstellung von Klassenzahlen als Perioden von Integralen 3. Gat- tung aus dem Gebiet der elliptischen Modulfunktionen, Mathematische Werke, Göttingen, Vandenhoeck & Ruprecht, 1959, 405-417. | JFM | MR
-[Hi1] Topological methods in algebraic geometry, Springer-Verlag, Berlin, 1966. | MR | Zbl
-[Hi2] Hilbert modular surfaces, Enseignement Math. 19, 183-281 (1973). | MR | Zbl
-[K1] Perturbation theory for linear operators, Berlin, Heidelberg, New York, Springer 1980. | Zbl
-[K2] Wave operators and unitary equivalence, Pacific J Math. 15, 171-180 (1965). | MR | Zbl
-[La] Signature des variétés modulaires de Hilbert et représentations diédrales, Lect. Notes in Math. 1447, 249-260, Springer-Verlag, Berlin 1990. | MR | Zbl
-[Me] The Atiyah-Patodi-Singer index theorem, A.K. Peters, Boston, 1993. | MR | Zbl
-[MP] Families of Dirac operators, boundaries and the -calculus, Preprint, MIT, 1994. | MR
and -[Mo] -index of elliptic operators on locally symmetric spaces of finite volume, Contemporary Math. 10, 129-137 (1982). | MR | Zbl
-[Mü1] Spectral theory for noncompact Riemannian manifolds with cusps and a related trace formula, I.H.E.S.-Preprint, Nr. 46, 1980.
-[Mü2] Signature defects of cusps of Hilbert modular varieties and values of -series at , J. Diff. Geom. 20, 55-119 (1984). | MR | Zbl
-[Mü3] Manifolds with cusps of rank one, Lect. Notes in Math. 1244, Springer-Verlag, Berlin, 1987. | MR | Zbl
-[Mü4] -index theory, eta invariants, and values of -functions, Contemporary Math. 105, 145-189 (1990). | DOI | MR | Zbl
-[Mü5] Eta invariants and manifolds with boundary. MPI-Preprint, 93-50, Bonn, 1993. | MR | Zbl
.[Mü6] -index and resonances, in: Analysis on manifolds (Katata 1987), pp. 203-211, Lect. Notes in Math. 1339, Springer, Berlin-New York, 1988. | MR | Zbl
-[O] Hirzebruch conjecture on cusp singularities, Math. Annalen 296, 69-86 (1993). | DOI | EuDML | MR | Zbl
-[S] On numerical invariants of arithmetic varieties of -rank one, in: "Automorphic forms of several variables", Taniguchi Symposium, Katata, 1983 (I. Satake and Y. Morita eds.), Adv. Studies in Pure Math. 46, Birkhäuser, Basel, 1984, 353-369. | MR | Zbl
-[SO] Zeta functions associated to cones and their special values, in: "Automorphic forms and geometry of arithmetic varieties" (Y. Namikawa and K. Hashimodo eds), Adv. Studies in Pure Math. 15, Kinokuniya, Tokyo and North-Holland, Amsterdam, New York, Oxford, 1989, 1-27. | MR | Zbl
and -[Sh] On discontinuous groups operating on the product of upper halfplanes, Ann. of Math. 77, 33-71 (1963). | DOI | MR | Zbl
-[St1] -index theorems on warped products, Princeton University Ph.D. thesis, October 1984.
-[St2] -index theorems on locally symmetric spaces, Invent. math. 96, 231-282 (1989). | DOI | EuDML | MR | Zbl
-[St3] Eta invariants and hermitian locally symmetric spaces, J. Diff. Geom. 31, 771-789 (1990). | DOI | MR | Zbl
-[St4] Lefschetz formulae for arithmetic varieties, Invent. math. 115, 241-296 (1994). | DOI | EuDML | MR | Zbl
-[W1] Global gravitational anomalies, Commun. Math. Phys. 100, 197-229 (1985). | DOI | MR | Zbl
-[W2] Global anomalies in string theory, in: Proc. of the Symposium on Anomalies, Geometry, Topology of Chicago (1985), Bardeen, W.A., White, A.R. (eds.), Singapore, World Scientific, 1985, pp. 61-99. | MR | Zbl
-