On the calculation of UNil
Algebraic Topology
2007-05-23 v2 K-Theory and Homology
Abstract
Cappell's codimension 1 splitting obstruction surgery group UNil_n(R;R,R) of a ring with involution R is a direct summand of the Wall surgery obstruction group L_n(R[D_{\infty}]) of the amalgamated free product R[D_{\infty}] = R[Z_2]*_RR[Z_2], with D_{\infty}=Z_2*Z_2 the infinite dihedral group. We use the quadratic Poincar\'e cobordism formulation of the L-groups to prove that L_n(R[x]) = L_n(R)\oplus UNil_n(R;R,R), with \bar{x} = x . We combine this with M. Weiss' universal chain bundle theory to produce almost complete calculations of UNil_*(Z;Z,Z) and L_*(Z[D_{\infty}]).
Cite
@article{arxiv.math/0304016,
title = {On the calculation of UNil},
author = {Frank Connolly and Andrew Ranicki},
journal= {arXiv preprint arXiv:math/0304016},
year = {2007}
}
Comments
48 pages, LATEX. Final version, to appear in Advances in Mathematics