Induced map on K theory for certain \Gamma-equivariant maps between Hilbert spaces

TL;DR

This paper develops an induced Clifford algebra framework for maps between Hilbert spaces, extending K-theory tools and computing specific K-groups to advance algebraic topology in infinite dimensions.

Contribution

It introduces an induced Hilbert Clifford algebra and constructs an induced K-theory map, extending the Higson-Kasparov-Trout approach to a broader class of Hilbert space maps.

Findings

Constructed an induced map between K-theories of Clifford algebras.

Computed K-groups for specific cases, demonstrating the framework's applicability.

Extended Bott periodicity results to new infinite-dimensional settings.

Abstract

Higson-Kapsparov-Trout introduced an infinite-dimensional Clifford algebra of a Hilbert space, and verified Bott periodicity on K-theory. To develop algebraic topology of maps between Hilbert spaces, in this paper we introduce an induced Hilbert Clifford algebra, and construct an induced map between K-theory of the Higson-Kasparov-Trout Clifford algebra and the induced Clifford algebra. We also compute its K-group for some concrete case.