Geodesic
The $K$-theory of endomorphisms of spaces
Homology, homotopy, and applications, Tome 18 (2016) no. 1, pp. 325-338.

Voir la notice de l'article provenant de la source International Press of Boston

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 $\mathbb{N}$-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.
DOI : 10.4310/HHA.2016.v18.n1.a17
Classification : 19D10, 19D35, 55N15
Keywords: $K$-theory of endomorphisms, algebraic $K$-theory of spaces, non-linear projective line. 
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     author = {Filipp Levikov},
     title = {The $K$-theory of endomorphisms of spaces},
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     pages = {325--338},
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     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.4310/HHA.2016.v18.n1.a17/}
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Filipp Levikov. The $K$-theory of endomorphisms of spaces. Homology, homotopy, and applications, Tome 18 (2016) no. 1, pp. 325-338. doi : 10.4310/HHA.2016.v18.n1.a17. http://geodesic.mathdoc.fr/articles/10.4310/HHA.2016.v18.n1.a17/

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