Calculation of UNil for the cyclic group of order two

TL;DR

This paper computes the UNil groups for the integral group ring of the cyclic group of order two, using algebraic methods to determine their structure as modules over the Verschiebung algebra.

Contribution

It provides the first explicit calculation of UNil(R;R,R) for Z[C_2], advancing understanding of algebraic K-theory for group rings.

Findings

UNil groups are determined as modules over the Verschiebung algebra

The calculation employs the Connolly--Ranicki isomorphism

Results clarify the structure of UNil for Z[C_2]

Abstract

Cappell's unitary nilpotent groups UNil(R;R,R) are calculated for the integral group ring R=Z[C_2] of the cyclic group C_2 of order two. Specifically, they are determined as modules over the Verschiebung algebra V using the Connolly--Ranicki isomorphism and the Connolly--Davis relations.