nLab index theory - contents

index theory, KK-theory

noncommutative topology, noncommutative geometry

noncommutative stable homotopy theory

partition function

genus, orientation in generalized cohomology

Definitions

operator K-theory

• C*-algebra

• Hilbert module

K-homology

• Fredholm operator

• differential operator, pseudodifferential operator

  • symbol of a differential operator

  • elliptic operator, elliptic complex

• Dirac operator

  • Spin^c Dirac operator

Index theorems

• topological index, analytical index

• Atiyah-Singer index theorem

  • Gauss-Bonnet theorem

  • Hirzebruch-Riemann-Roch theorem

  • global analytic index theory

  • Hirzebruch signature theorem

• Mishchenko-Fomenko index theorem

• Baum-Connes conjecture

Higher genera

• elliptic genus

• Witten genus