The K-theory of endomorphisms of spaces

Filipp Levikov

The K-theory of endomorphisms of spaces

K-Theory and Homology 2015-11-30 v1 Algebraic Topology

Authors: Filipp Levikov

Abstract

We prove a non-linear version of a theorem of Grayson which is an analogue of the Fundamental Theorem of Algebraic $K$ -theory and identify the $K$ -theory of the endomorphism category over a space $X$ in terms of reduced $K$ -theory of a certain localisation of the category of $\NN$ -spaces over $X$ . In particular we generalise the result of Klein and Williams describing the nil-terms of $A$ -theory in terms of $K$ -theory of nilpotent endomorphisms.

Keywords

algebraic K-theory endomorphism categories spaces Grayson theorem localization nil-terms A-theory

Cite

@article{arxiv.1511.08376,
  title  = {The K-theory of endomorphisms of spaces},
  author = {Filipp Levikov},
  journal= {arXiv preprint arXiv:1511.08376},
  year   = {2015}
}

Comments

14 pages; uses Paul Taylor's diagrams.sty; to appear in Homology, Homotopy and Applications

The K-theory of endomorphisms of spaces

Abstract

Keywords

Cite

Comments

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