TOPOLOGICAL INVARIANTS OF ELLIPTIC OPERATORS. I:K-HOMOLOGY

1975/08/31 by Gennadi Kasparov · 4 citations
Mathematics · #Homotopy and Cohomology in Algebraic Topology #Advanced Topics in Algebra #Advanced Operator Algebra Research #Mathematics #Functor #Pure mathematics #Atiyah–Singer index theorem #Homology (biology) #Axiom #Generalization #Algebra over a field #Discrete mathematics #Mathematical analysis

paper · doi:10.1070/im1975v009n04abeh001497

openalex publication_date 1975/08/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/31

Abstract

In this paper the homological K -functor is defined on the category of involutory Banach algebras, and Bott periodicity is proved, along with a series of theorems corresponding to the Eilenberg-Steenrod axioms. As an application, a generalization of the Atiyah-Singer index theorem is obtained,and some problems connected with representation rings of discrete groups and higher signatures of smooth manifolds are discussed. Bibliography: 16 items.

Citations

• BOTT PERIODICITY AND THE INDEX OF ELLIPTIC OPERATORS
• The Index of Elliptic Operators: I
• The Index of Elliptic Operators: IV
• The Index of Elliptic Operators: V

Cited by

• The index of signature operators on Lipschitz manifolds
• The index theorem for topological manifolds
• Geometric K-homology with coefficients I
• Atiyah–Singer index theorem [wikipedia]