Abstract
For given closed orientable –manifolds and let be the set of mapping degrees from to . We address the problem: For which is finite for all ? The answer is known for prime –manifolds unless the target is a nontrivial graph manifold. We prove that for each closed nontrivial graph manifold , is finite for any graph manifold .
The proof uses a recently developed standard form of maps between graph manifolds and the estimation of the –volume for a certain class of graph manifolds.
Citation
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. https://doi.org/10.2140/agt.2009.9.1727
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