index theory, KK-theory

noncommutative topology, noncommutative geometry

noncommutative stable homotopy theory

partition function

genus, orientation in generalized cohomology

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

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

elliptic genus

Witten genus