The spectral model of (Real) $K$-theory

Anupam Datta

The spectral model of (Real) $K$-theory

K-Theory and Homology 2024-10-30 v1 Operator Algebras

Authors: Anupam Datta

Abstract

We use homotopy theoretic ideas to study the $K$ -theory of (graded, Real) $C^*$ -algebras in detail. After laying the foundations, and deriving the formal properties, the comparison of the model with the Kasparov picture of $K$ -theory has been made, and Bott periodicity has been proven using a Dirac-dual Dirac method.

Keywords

K-theory C*-algebra homotopy theory Kasparov picture Bott periodicity

Cite

@article{arxiv.2410.21606,
  title  = {The spectral model of (Real) $K$-theory},
  author = {Anupam Datta},
  journal= {arXiv preprint arXiv:2410.21606},
  year   = {2024}
}

Comments

This article is roughly the content of the author's masters thesis written under the supervision of Prof. Dr. Johannes Ebert at the University of Muenster in 2023. An updated version will be available at a later date

The spectral model of (Real) $K$-theory

Abstract

Keywords

Cite

Comments

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