Eta invariants and complex immersions

Jean-Michel Bismut

Bulletin de la Société Mathématique de France (1990)

  • Volume: 118, Issue: 2, page 211-227
  • ISSN: 0037-9484

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Bismut, Jean-Michel. "Eta invariants and complex immersions." Bulletin de la Société Mathématique de France 118.2 (1990): 211-227. <http://eudml.org/doc/87602>.

@article{Bismut1990,
author = {Bismut, Jean-Michel},
journal = {Bulletin de la Société Mathématique de France},
keywords = {holonomy of line bundles; embedding of complex manifolds; eta invariant; holomorphic submersions; holomorphic Hermitian connections; Quillen metrics},
language = {eng},
number = {2},
pages = {211-227},
publisher = {Société mathématique de France},
title = {Eta invariants and complex immersions},
url = {http://eudml.org/doc/87602},
volume = {118},
year = {1990},
}

TY - JOUR
AU - Bismut, Jean-Michel
TI - Eta invariants and complex immersions
JO - Bulletin de la Société Mathématique de France
PY - 1990
PB - Société mathématique de France
VL - 118
IS - 2
SP - 211
EP - 227
LA - eng
KW - holonomy of line bundles; embedding of complex manifolds; eta invariant; holomorphic submersions; holomorphic Hermitian connections; Quillen metrics
UR - http://eudml.org/doc/87602
ER -

References

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  1. [APS] ATIYAH (M.F.), PATODI (V.K.), and SINGER (I.M.). — Spectral asymmetry and Riemannian geometry, I. Math. Proc. Camb. Phil. Soc., t. 77, 1975, p. 43-69. Zbl0297.58008MR53 #1655a
  2. [B] BISMUT (J.M.). — Superconnection currents and complex immersions, Invent. Math., t. 99, 1990, p. 59-113. Zbl0696.58006MR91b:58240
  3. [BBos] BISMUT (J.M.) and BOST (J.B.). — Métriques de Quillen et dégénérescence des courbes, preprint IHES M/88/48, To appear in Acta Mathematica. 
  4. [BF] BISMUT (J.M.) and FREED (D.S.). — The analysis of elliptic families II, Comm. Math. Phys., t. 107, 1986, p. 103-163. Zbl0657.58038MR88h:58110b
  5. [BGS1] BISMUT (J.M.), GILLET (H.) and SOULÉ (C.). — Bott-Chern currents and complex immersions, Duke Math. J., t. 60, 1990, p. 255-284. Zbl0697.58005MR91d:58239
  6. [BGS2] BISMUT (J.M.), GILLET (H.) and SOULÉ (C.). — Complex immersions and Arakelov geometry, preprint IHES M/88/44. Zbl0744.14015
  7. [BGS3] BISMUT (J.M.), GILLET (H.) and SOULÉ (C.). — Analytic torsion and holomorphic determinant bundles III, Comm. Math. Phys., t. 115, 1988, p. 301-351. Zbl0651.32017MR89g:58192c
  8. [BL] BISMUT (J.M.), LEBEAU (G.). — Complex immersions and Quillen metrics, preprint Orsay, 1990. 
  9. [CSi] CHEEGER (J.) and SIMONS (J.). — Differential characters and geometric invariants, in Geometry and Topology, [J. Alexander and J. Harer ed.], p. 50-80, Lecture Notes in Math., n° 1167, Berlin-Heidelberg-New York, Springer, 1985. Zbl0621.57010MR87g:53059
  10. [E] EILENBERG (S.). — Homological dimension and local syzygies., Annals of Math., t. 64, 1956, p. 328-336. Zbl0073.26003MR18,558c
  11. [GS] GILLET (H.), SOULÉ (C.). — Arithmetic Chow groups and differential characters, in Algebraic K-theory, Connections with geometry and topology, [J.F. Jardine and V.P. Snaith, ed.], Kluwer Academic Publishers, 1989. Zbl0719.14003MR91j:14017
  12. [H] HITCHIN (N.). — Harmonic spinors, Adv. Math., t. 14, 1974, p. 1-55. Zbl0284.58016MR50 #11332
  13. [KM] KNUDSEN (F.F.) and MUMFORD (V.). — The projectivity of the moduli space of stable curves I, Preliminaries on det and div, Math. Scand., t. 39, 1976, p. 19-55. Zbl0343.14008
  14. [Q1] QUILLEN (D.). — Superconnections and the Chern character, Topology, t. 24, 1985, p. 89-95. Zbl0569.58030MR86m:58010
  15. [Q2] QUILLEN (D.). — Determinants of Cauchy-Riemann operators over a Riemann surface, Funct. Anal. Appl., t. 19, 1985, p. 31-34. Zbl0603.32016MR86g:32035
  16. [Se] SERRE (J.P.). — Algèbre locale. Multiplicités, Lecture Notes in Math., n° 11, Berlin-Heidelberg-New York, Springer, 1965. Zbl0142.28603MR34 #1352

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