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
Hirzebruch signature theorem?
Mishchenko-Fomenko index theorem
Baum-Connes conjecture
elliptic genus
Witten genus