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2009 Finiteness of mapping degrees and ${\rm PSL}(2,\mathbf{R})$–volume on graph manifolds
Pierre Derbez, Shicheng Wang
Algebr. Geom. Topol. 9(3): 1727-1749 (2009). DOI: 10.2140/agt.2009.9.1727


For given closed orientable 3–manifolds M and N let D(M,N) be the set of mapping degrees from M to N. We address the problem: For which N is D(M,N) finite for all M? The answer is known for prime 3–manifolds unless the target is a nontrivial graph manifold. We prove that for each closed nontrivial graph manifold N, D(M,N) is finite for any graph manifold M.

The proof uses a recently developed standard form of maps between graph manifolds and the estimation of the PSL˜(2,R)–volume for a certain class of graph manifolds.


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Pierre Derbez. Shicheng Wang. "Finiteness of mapping degrees and ${\rm PSL}(2,\mathbf{R})$–volume on graph manifolds." Algebr. Geom. Topol. 9 (3) 1727 - 1749, 2009.


Received: 23 March 2009; Revised: 17 July 2009; Accepted: 27 July 2009; Published: 2009
First available in Project Euclid: 20 December 2017

zbMATH: 1187.57021
MathSciNet: MR2539193
Digital Object Identifier: 10.2140/agt.2009.9.1727

Primary: 57M50
Secondary: 51H20

Keywords: graph manifold , nonzero degree maps , volume of a representation

Rights: Copyright © 2009 Mathematical Sciences Publishers


Vol.9 • No. 3 • 2009
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