Finiteness of mapping degrees and ${\rm PSL}(2,{\R})$-volume on graph manifolds

dc.creatorDerbez, Pierre
dc.creatorWang, Shicheng
dc.date2008-01-13
dc.date2008-10-14
dc.date.accessioned2026-07-07T10:09:17Z
dc.date.available2026-07-07T10:09:17Z
dc.descriptionFor 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.description15 pages 4 figures
dc.identifierhttps://arxiv.org/abs/0801.1946
dc.identifierhttp://arxiv.org/abs/0801.1946
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/171273
dc.subjectGeometric Topology
dc.subjectAlgebraic Topology
dc.subject57M50, 57M10, 55M20, 51H20
dc.titleFiniteness of mapping degrees and ${\rm PSL}(2,{\R})$-volume on graph manifolds
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