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

2008/01/13 by Pierre Derbez, Derbez, Pierre, Shicheng Wang +1 · 1 citation
Mathematics · #51H20 #55M20 #57M10 #57M50 #Algebraic Topology (math.AT) #FOS: Mathematics #Geometric Topology (math.GT) #math.AT #math.GT #msc:51H20 #msc:55M20 #msc:57M10 #msc:57M50

paper · pdf · doi:10.48550/arxiv.0801.1946

15 pages 4 figures

arxiv created 2008/10/14 · arxiv updated 2009/12/01

Abstract

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.

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