Clifford modules and twisted K-theory
Max Karoubi (Paris University)
TL;DR
This paper explicitly links the foundational work of Atiyah, Bott, and Shapiro to twisted K-theory, clarifying an implicit connection in the literature that was previously not formally defined.
Contribution
It formally establishes the connection between classical Clifford module theory and modern twisted K-theory, filling a gap in the theoretical framework.
Findings
Explicitly defines the link between Clifford modules and twisted K-theory
Clarifies the real K-theory of spheres within this framework
Bridges historical and modern perspectives in K-theory
Abstract
The purpose of this shord paper is to make the link between the fundamental work of Atiyah, Bott and Shapiro (MR0167985/29/5250) and twisted K-theory (MR0282363/43/8075). This link was implicit for a long time in the literature (for the description of the real K-theory of spheres as an example) but was not explicitly defined before.
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Taxonomy
TopicsHomotopy and Cohomology in Algebraic Topology · Topological and Geometric Data Analysis · Geometric and Algebraic Topology