Finiteness of mapping degrees and ${\rm PSL}(2,{\R})$-volume on graph manifolds
| dc.creator | Derbez, Pierre | |
| dc.creator | Wang, Shicheng | |
| dc.date | 2008-01-13 | |
| dc.date | 2008-10-14 | |
| dc.date.accessioned | 2026-07-07T10:09:17Z | |
| dc.date.available | 2026-07-07T10:09:17Z | |
| dc.description | For given closed orientable 3-manifolds $M$ and $N$ let $cD(M,N)$ be the set of mapping degrees from $M$ to $N$. We address the problem: For which $N$, $cD(M,N)$ is finite for all $M$? The answer is known in Thurston's picture of closed orientable irreducible 3-manifolds unless the target is a non-trivial graph manifold. We prove that for each closed non-trivial graph manifold $N$, $cD(M,N)$ is finite for all graph manifold $M$. The proof uses a recently developed standard forms of maps between graph manifolds and the estimation of the $\widetilde{\rm PSL}(2,{\R})$-volume for certain class of graph manifolds. | |
| dc.description | 15 pages 4 figures | |
| dc.identifier | https://arxiv.org/abs/0801.1946 | |
| dc.identifier | http://arxiv.org/abs/0801.1946 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/171273 | |
| dc.subject | Geometric Topology | |
| dc.subject | Algebraic Topology | |
| dc.subject | 57M50, 57M10, 55M20, 51H20 | |
| dc.title | Finiteness of mapping degrees and ${\rm PSL}(2,{\R})$-volume on graph manifolds | |
| dc.type | text |