On $π- π$ theorem for manifold pairs with boundaries
| dc.creator | Cencelj, M. | |
| dc.creator | Muranov, Yu. V. | |
| dc.creator | Repovš, D. | |
| dc.date | 2007-05-29 | |
| dc.date.accessioned | 2026-07-07T08:03:28Z | |
| dc.date.available | 2026-07-07T08:03:28Z | |
| dc.description | Surgery obstruction of a normal map to a simple Poincare pair $(X,Y)$ lies in the relative surgery obstruction group $L_*(π_1(Y)\toπ_1(X))$. A well known result of Wall, the so called $π$-$π$ theorem, states that in higher dimensions a normal map of a manifold with boundary to a simple Poincare pair with $π_1(X)\congπ_1(Y)$ is normally bordant to a simple homotopy equivalence of pairs. In order to study normal maps to a manifold with a submanifold, Wall introduced surgery obstruction group for manifold pairs $LP_*$ and splitting obstruction groups $LS_*$. In the present paper we formulate and prove for manifold pairs with boundaries the results which are similar to the $π$-$π$ theorem. We give direct geometric proofs, which are based on the original statements of Wall's results and apply obtained results to investigate surgery on filtered manifolds. | |
| dc.identifier | https://arxiv.org/abs/0705.4155 | |
| dc.identifier | http://arxiv.org/abs/0705.4155 | |
| dc.identifier | Mathematical Notes 81: 3-4 (2007), 356-364 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/129589 | |
| dc.subject | Geometric Topology | |
| dc.subject | Algebraic Topology | |
| dc.subject | 57R67, 57Q10, 57R10, 55U35 | |
| dc.title | On $π- π$ theorem for manifold pairs with boundaries | |
| dc.type | text |