Geodesic
Finiteness of mapping degrees and PSL(2,R)–volume on graph manifolds
Derbez, Pierre1 ; Wang, Shicheng2
1CMI, Technopôle Château-Gombert, 39 rue Joliot Curie, 13453 Marseille Cedex 13, France
2Department of Mathematics, Peking University, Beijing, 100871, China
Algebraic and Geometric Topology, Tome 9 (2009) no. 3, pp. 1727-1749
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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.

DOI : 10.2140/agt.2009.9.1727
Keywords: graph manifold, nonzero degree maps, volume of a representation

Derbez, Pierre  1   ; Wang, Shicheng  2

1 CMI, Technopôle Château-Gombert, 39 rue Joliot Curie, 13453 Marseille Cedex 13, France
2 Department of Mathematics, Peking University, Beijing, 100871, China 
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Derbez, Pierre; Wang, Shicheng. Finiteness of mapping degrees and PSL(2,R)–volume on graph manifolds. Algebraic and Geometric Topology, Tome 9 (2009) no. 3, pp. 1727-1749. doi: 10.2140/agt.2009.9.1727

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