Degree-one maps, surgery and four-manifolds
| dc.creator | Gadgil, Siddhartha | |
| dc.date | 2008-09-18 | |
| dc.date.accessioned | 2026-07-07T10:03:42Z | |
| dc.date.available | 2026-07-07T10:03:42Z | |
| dc.description | We give a description of degree-one maps between closed, oriented 3-manifolds in terms of surgery. Namely, we show that there is a degree-one map from a closed, oriented 3-manifold $M$ to a closed, oriented 3-manifold $N$ if and only if $M$ can be obtained from $N$ by surgery about a link in $N$ each of whose components is an unknot. We use this to interpret the existence of degree-one maps between closed 3-manifolds in terms of smooth 4-manifolds. More precisely, we show that there is a degree-one map from $M$ to $N$ if and only if there is a smooth embedding of $M$ in $W=(N\times I)#_n \bar{\C P^2}#_m {\C P^2}$, for some $m\geq 0$, $n\geq 0$ which separates the boundary components of $W$. This is motivated by the relation to topological field theories, in particular the invariants of Ozsvath and Szabo. | |
| dc.description | 11 pages | |
| dc.identifier | https://arxiv.org/abs/0809.3102 | |
| dc.identifier | http://arxiv.org/abs/0809.3102 | |
| dc.identifier | Bull. Lond. Math. Soc. 39 (2007), no. 3, 419--424 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/169388 | |
| dc.subject | Geometric Topology | |
| dc.subject | 57N10; 57N13, 57M27 | |
| dc.title | Degree-one maps, surgery and four-manifolds | |
| dc.type | text |