Introduction à l’invariant η
Séminaire de théorie spectrale et géométrie, Tome 7 (1988-1989), pp. 103-114. 
@article{TSG_1988-1989__7__103_0,
     author = {Guillop\'e, Laurent},
     title = {Introduction \`a l{\textquoteright}invariant $\eta $},
     journal = {S\'eminaire de th\'eorie spectrale et g\'eom\'etrie},
     pages = {103--114},
     publisher = {Institut Fourier},
     address = {Grenoble},
     volume = {7},
     year = {1988-1989},
     mrnumber = {1046269},
     zbl = {0706.58073},
     language = {fr},
     url = {http://www.numdam.org/item/TSG_1988-1989__7__103_0/}
}
TY  - JOUR
AU  - Guillopé, Laurent
TI  - Introduction à l’invariant $\eta $
JO  - Séminaire de théorie spectrale et géométrie
PY  - 1988-1989
SP  - 103
EP  - 114
VL  - 7
PB  - Institut Fourier
PP  - Grenoble
UR  - http://www.numdam.org/item/TSG_1988-1989__7__103_0/
LA  - fr
ID  - TSG_1988-1989__7__103_0
ER  - 
%0 Journal Article
%A Guillopé, Laurent
%T Introduction à l’invariant $\eta $
%J Séminaire de théorie spectrale et géométrie
%D 1988-1989
%P 103-114
%V 7
%I Institut Fourier
%C Grenoble
%U http://www.numdam.org/item/TSG_1988-1989__7__103_0/
%G fr
%F TSG_1988-1989__7__103_0
Guillopé, Laurent. Introduction à l’invariant $\eta $. Séminaire de théorie spectrale et géométrie, Tome 7 (1988-1989), pp. 103-114. http://www.numdam.org/item/TSG_1988-1989__7__103_0/

[1] Atiyaii M., Patodi V., Singer L. - Spectral asymmetry and riemannian geometry I., Mat. Proc. Camb. Soc., 77 ( 1975), 43-69. | MR | Zbl

[2] Gilkey P. - Invariance theory, the heat equation and the Atiyah-Singer index theorem, Publish or Perish, Wilmington, 1984. | MR | Zbl

[3] Hörmander L. - The analysis of linear partial differential operators III, Springer Verlag, Berlin, 1985. | MR | Zbl

[4] Husemoller D. - Fibre bundies, Springer Verlag, Berlin, 1974. | Zbl

[5] Seeley R. - Complex powers of an elliptic operator, Proc. Symp. in Pure Math., 10 ( 1967), 288-307. | MR | Zbl

[6] Wodzicki M. - Spectral asymmetry and zeta functions , Inv. Math., 66 ( 1982), 115-135. | MR | Zbl

[1] Atiyah M. - The logarithm of the Dedekind n-function, Math. Ann., 278 ( 1987), 335-380. | MR | Zbl

[2] Atiyah M., Donnelly H., Singer I. - Geometry and analysis of Shimizu L-functions, Proc. Nat Acad. Sci. USA, 79 ( 1982), 5751-5752. | MR | Zbl

[3] Atiyah M., Donnelly H., Singer I. - Eta invariants, signature defects of cusps and values of L-functions, Ann. Math., 118 ( 1983), 131-177. | MR | Zbl

[4] Atiyah M., Patodi V., Slnger I. - Spectral asymmetry and riemannian geometry. Buil. London Math. Soc., 5 ( 1973). 229-234. | MR | Zbl

[5] Atiyah M., Patodi V., Slnger I. - Spectral asymmetry and riemannian geometry I, Mat. Proc. Camb. Soc., 77 ( 1975), 43-69. | MR | Zbl

[6] Atiyah M. , Patodi V. , Singer I. - Spectral asymmetry and riemannian geometry II, Mat. Proc. Camb. Soc, 78 ( 1975), 405-432. | MR | Zbl

[7] Atiyah M., Patodi V., Slnger L. - Spectral asymmetry and riemannian geometry III, Mat. Proc. Camb. Soc, 79 ( 1976), 71-99. | MR | Zbl

[8] Blsmut J-M. , Bost J-B. - Fibrés déterminants, métriques de Quillen et dégénérescence des courbes, Preprint I.H.E.S, ( 1988). | MR | Zbl

[9] Bismut J-M. , Cheeger J. - Invariants êta et indice des familles pour des variétés à bord, C.R. Acad. Sci. Paris, 305 ( 1987). 127-130. | MR | Zbl

[10] Bismut J-M. , Cheeger J. - Families index for manifolds with boundary, superconnections and cones, A paraître dans J. Func. Anal., ( 1989). | Zbl

[11] Bismut J-M. , Cheeger J. - n-invariants and their adiabatic limits, J. Amer. Math. Soc, 2 ( 1989), 33-70. | MR | Zbl

[12] Bismut J-M. , Freed D. - The analysis of elliptic families II. Dirac operators, êta invariants and the holonomy theorem. Commun. Math. Phys., 107 ( 1986), 103-163. | MR | Zbl

[13] Brunin G.J., Seeley R. - An index theorem for regular singular operators. Amer. J. Math., ( 1987).

[14] Brüning J. - L2-index theorems for certain complete manifolds, A paraître dans J. Differential Geo., 0. | Zbl

[15] Burghelea D., Kappeler T. - On the determinant for elliptic differential operators in vector bundies over S1, Preprint, ( 1989). | Zbl

[16] Cheeger J. - Spectral geometry of singular Riemannian spaces, J. Differential Geo., 18 ( 1983), 575-657. | MR | Zbl

[17] Cheeger J., Gromov M. - On the characteristic numbers of complete manifolds of bounded curvature and finite volume. Differential geometry and complex analysis, Vol. dedicated to H. E. RAUCH , ( 1985), 115-154. | MR | Zbl

[18] Cheeger J. - Eta invariants, the adiabatic aproximation and cortical singularities, J. Differential Geo., 26 ( 1987), 175-221. | MR | Zbl

[19] Chou A.W. - The Dirac operator on spaces with conical singularities and positive curvatures, Tans. Amer. Math. Soc., 289 ( 1985), 1-40. | MR | Zbl

[20] Dai X. - Ph. D. Thesis, SUNY at Stony Brook, (),.

[21] Donnelly H. - Spectral geometry and invariants from differential topology, Bull. London Math. Soc, 5 ( 1975). 147-150. | MR | Zbl

[22] Donnelly H. - Eta invariant of a fibered manifold, Topology, 15 ( 1976), 247-252. | MR | Zbl

[23] Donnelly H. - Eta invariants for G-spaces, Indiana Univ. Math. J., 27 ( 1978), 899-918. | MR | Zbl

[24] Douglas R. - Elliptic invariants for differential operators, Proceedings in Pure mathematics, 48 ( 1988), 275-285. | MR | Zbl

[25] Douglas R., Hurder S., Kaminker J. - Toeplitz operators and the eta invariant : the case of S1, Index theory of elliptic operators, foliation and operator algebras, Contemporary mathematics, 70 ( 1988), 11-42. | MR | Zbl

[26] Douglas R., Wojciechowski K. - Spectral flow of families of elliplic boudary value problems and adiabatic limits of the n-invariants, preprint, 0.

[27] Gllkey P. - The residue of the local eta fonction at the origin. Math. Ann., 240 ( 1979), 183-189. | MR | Zbl

[28] Gilkey P. - The residue of the global eta function al the origin, Adv. in Math., 40 ( 1981), 290-307. | MR | Zbl

[29] Gilkey P. - Invariance theory, the heat equation and the Atiyah-Singer index theorem, Publish or Perish, Wilmington, 1984. | MR | Zbl

[30] Gilkey P. - The eta invariant and second characteristic classes of locally flat bundies, Algebraic and differential topology, global differemial geometry, Texte zur Math., Teubner, Leipzig, 70 ( 1984), 49-88. | MR | Zbl

[31] Gilkey P. - The eta invariant and the K-theory of odd dimensional spherical space forms, Inv. Math., 76 ( 1984), 421-453. | MR | Zbl

[32] Gilkey P. - The eta invariant for even dimensional Pinc-manifolds, Adv. in Malh., 58 ( 1985), 243-284. | MR | Zbl

[33] Gilkey P. - The eta invariant and KO of lens spaces. Malh. Zeitschrift, 194 ( 1987), 309-320. | MR | Zbl

[34] Gilkey P. , Smith L. - The eta invariant for a class of elliptic boundary value problems, Comm. Pure Appl. Math., 36 ( 1983), 85-132. | MR | Zbl

[35] Gilkey P. , Smith L. - The twisted index theorem for manifolds with boundary, J. Differemial Geo., 18 ( 1983), 393-444. | MR | Zbl

[36] Kassel. - Le résidu non commutatif (d'après M. Wodzicki), séminaire Bourbaki, ( 1989). | Numdam | Zbl

[37] Katase K. - Eta function on three-sphere, Proc. Japan Acad. Ser. A Math. Sci., 57 ( 1981), 233-237. | MR | Zbl

[38] Komuro M. - On Atiyah-Patodi-Singer eta invariants for S1-bundles over Riemann surfaces, J. Fac. Sci. Univ. Tokyo Sect. 1A Math., 30 ( 1984), 525-548. | MR | Zbl

[39] Kreck M., Stolz S. - A diffeomorphism classification of 7-dimensional homogenous Einstein manifolds with SU(3) x SU(2) x U(1)-symmetry, Ann. Math., 127 ( 1988), 373-388. | MR | Zbl

[40] Lazarov C. - Spectral invariants for foliations, Michigan J. Math., 33 ( 1986), 231-243. | MR | Zbl

[41] Lazarov C. - A relation between index and exotic classes, Index theory of elliptic operators, foliation and operator algebras, Contemporary mathematics, 70 ( 1988), 125-144. | MR | Zbl

[42] Mazzeo R., Melrose R. - The adiabatic limit, Hodge cohomology and the Leroy's spectral sequence of a fibration, preprint, ( 1988). | Zbl

[43] Millson J. - Closed geodesics and the eta invariant, Ann. Math., 108 ( 1978), 1-39. | MR | Zbl

[44] Moscovici H., Stanton R. - Eta invariants of Dirac operators on locally symmetrie manifolds, Inv. Math., 95 ( 1987), 629-666. | MR | Zbl

[45] Muller W. - Signature defects of cusps of Hilbert modular surfaces and values of L-functions at s = 1, J. Differential Geo., 20 ( 1984), 55-119. | MR | Zbl

[46] Muller W. - Manifolds with cusps of rank one, Lecture notes in Math.1244, 1987. | MR | Zbl

[47] Muller W. - L2-index and resonances, Lecture notes in Math., 1339 ( 1988), 203-211. | MR | Zbl

[48] Muller W. - L2-index, eta invariants and values of L-functions, A paraître dans Contemp. Math, ().

[49] Singer L. - The n-invariant and the index, Proc. Conf. on string theory, University of California at San Diego, 1986. | Zbl

[50] Smith L. - The e invariant and finite covering, Indiana Univ. Math. J., 24 ( 1975), 659-675. | MR | Zbl

[51] Stern M. - L2-index theorems on locally symmetrie spaces, Inv. Math., 96 ( 1989), 231-282. | MR | Zbl

[52] Witten E. - Global gravitational anomalies, Commun. Math. Phys., 100 ( 1985), 197-229. | MR | Zbl

[53] Wodzicki M. - Local invariants of spectral asymmetry, Inv. Math., 75 ( 1984), 143-178. | MR | Zbl

[54] Wodzicki M. - Non commutative residues 1 : Fundamentals. K-Theory, arithmetic and geometry, séminaire, Moscou 1984-1986, Lecture notes in Math., 1289 ( 1987), 320-399. | Zbl

[55] Wodzicki M. - Spectral asymmetry and zeta fonctions , Inv. Math., 66 ( 1982), 115-135. | MR | Zbl

[56] Wojciechowski K. - Spectral asymmetry, elliptic boudary value problem, cutting and pasting of elliptic operators, ().

[57] Yoshida T. - The eta invariant of hyperbolic 3-manifolds, Inv. Math., 81 ( 1985), 473-514. | MR | Zbl