nLab index theorem

Entries

• index

  • analytical index

  • topological index

• index theorem

  • Atiyah-Singer index theorem

  • Mishchenko-Fomenko index theorem

  • microlocal formulation of index theory

Index theory naturally takes place in KK-theory.

References

• David Edwards, Lectures on index theory I, pdf, Lectures on index theory II, pdf, The Index Program for K-Theory with Local Coefficients, pdf
• Masaki Kashiwara, Pierre Schapira, Hochschild homology and microlocal Euler classes, arxiv/1203.4869

Exposition with an eye towards application in mathematical physics:

• Tohru Eguchi, Peter Gilkey, Andrew Hanson, Section 10.2 of: Gravitation, gauge theories and differential geometry, Physics Reports 66 6 (1980) 213-393 [doi:10.1016/0370-1573(80)90130-1]