The "fundamental theorem" for the algebraic K-theory of spaces. III. the nil-term

TL;DR

This paper characterizes the nil-terms in Waldhausen's algebraic K-theory of spaces as the reduced K-theory of a specific category of equivariant spaces with nilpotent endomorphisms, advancing understanding of algebraic K-theory structures.

Contribution

It provides a new description of nil-terms in algebraic K-theory of spaces using equivariant spaces with nilpotent endomorphisms, extending previous theoretical frameworks.

Findings

Nil-terms identified as reduced K-theory of equivariant spaces

Connection established between nil-terms and homotopically nilpotent endomorphisms

Advances the algebraic understanding of K-theory of spaces

Abstract

In this paper we identify the ``nil-terms'' for Waldhausen's algebraic K-theory of spaces functor as the reduced K-theory of a category of equivariant spaces equipped with a homotopically nilpotent endomorphism.