Calculation of UNil for the cyclic group of order two

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.

💡 Research Summary

The paper addresses the explicit computation of Cappell’s unitary nilpotent groups UNil(R; R,R) when the coefficient ring R is the integral group ring ℤ