The K-theory of endomorphisms of spaces

  title={The K-theory of endomorphisms of spaces},
  author={Filipp Levikov},
  journal={arXiv: K-Theory and Homology},
  • Filipp Levikov
  • Published 26 November 2015
  • Mathematics
  • arXiv: K-Theory and Homology
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. 
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