eta invariant




The η\eta-invariant was introduced by Atiyah-Patodi-Singer in the series of articles

  • Michael Atiyah, V. K. Patodi and Isadore Singer, Spectral asymmetry and Riemannian geometry I Proc. Cambridge Philos. Soc. 77 (1975), 43-69.

    Spectral asymmetry and Riemannian geometry II. Proc. Cambridge Philos. Soc.

    Spectral asymmetry and Riemannian geometry III, Proc. Cambridge Philos. Soc. 79 (1976), 71-99.

as the boundary correction term for the index formula? on a manifold with boundary.

Introductions and surveys include

  • Jean-Michel Bismut, Local index theory, eta invariants and holomorphic torsion: a survey, pp. 1-76, in: Surveys in diff. geom. (C. C Hsiang, S/T. Yau, eds.) 1998. International Press
  • Ken Richardson, Introduction to the Eta invariant (pdf)
  • Xianzhe Dai, Eta invariant and holonomy Chern Centennial (2011) (pdf slides)
  • Wikipedia, Eta invariant

Further discussion of the relation to holonomy is in

  • Xianzhe Dai, Weiping Zhang, Eta invariant and holonomy, the even dimensional case, arXiv:1205.0562

Eta invariants play role in

  • Lisa C. Jeffrey, Symplectic quantum mechanics and Chern=Simons gauge theory I, arxiv/1210.6635

Revised on November 1, 2012 01:02:25 by Zoran Škoda (