Non-zero degree maps between $2n$-manifolds
| dc.creator | Duan, Haibao | |
| dc.creator | Wang, Shicheng | |
| dc.date | 2004-02-08 | |
| dc.date.accessioned | 2026-07-07T05:05:14Z | |
| dc.date.available | 2026-07-07T05:05:14Z | |
| dc.description | Thom-Pontrjagin constructions are used to give a computable necessary and sufficient condition when a homomorphism $ϕ: H^n(L;Z)\to H^n(M;Z)$ can be realized by a map $f:M\to L$ of degree $k$ for closed $(n-1)$-connected $2n$-manifolds $M$ and $L$, $n>1$. A corollary is that each $(n-1)$-connected $2n$-manifold admits selfmaps of degree larger than 1, $n>1$. In the most interesting case of dimension 4, with the additional surgery arguments we give a necessary and sufficient condition for the existence of a degree $k$ map from a closed orientable 4-manifold $M$ to a closed simply connected 4-manifold $L$ in terms of their intersection forms, in particular there is a map $f:M\to L$ of degree 1 if and only if the intersection form of $L$ is isomorphic to a direct summand of that of $M$. | |
| dc.description | 18 pages | |
| dc.identifier | https://arxiv.org/abs/math/0402119 | |
| dc.identifier | http://arxiv.org/abs/math/0402119 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/70094 | |
| dc.subject | Geometric Topology | |
| dc.subject | Algebraic Topology | |
| dc.subject | 57R19; 55M25 | |
| dc.title | Non-zero degree maps between $2n$-manifolds | |
| dc.type | text |