On the calculation of UNil
| dc.creator | Connolly, Frank | |
| dc.creator | Ranicki, Andrew | |
| dc.date | 2003-04-02 | |
| dc.date | 2004-08-10 | |
| dc.date.accessioned | 2026-07-07T04:56:33Z | |
| dc.date.available | 2026-07-07T04:56:33Z | |
| dc.description | 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 Poincaré 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}]). | |
| dc.description | 48 pages, LATEX. Final version, to appear in Advances in Mathematics | |
| dc.identifier | https://arxiv.org/abs/math/0304016 | |
| dc.identifier | http://arxiv.org/abs/math/0304016 | |
| dc.identifier | Advances in Mathematics 195, 205--258 (2005) | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/66962 | |
| dc.subject | Algebraic Topology | |
| dc.subject | K-Theory and Homology | |
| dc.subject | 57N15, 57R67 | |
| dc.title | On the calculation of UNil | |
| dc.type | text |