The K-theory of endomorphisms of spaces

2015/11/26 by Levikov, Filipp
#19D10 #19D35 #55N15 #Algebraic Topology (math.AT) #FOS: Mathematics #K-Theory and Homology (math.KT)

paper · doi:10.48550/arxiv.1511.08376

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.

Related

• The "fundamental theorem" for the algebraic K-theory of spaces. III. the nil-term
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• A Theorem of the Heart for K-theory of Endomorphisms
• The K-Theory of Finitely Many Commuting Endomorphisms
• Frobenius and Verschiebung for K-theory of endomorphisms