Homomorphisms into mapping class groups. An addendum
Jason Behrstock, Cornelia Drutu, Mark Sapir

TL;DR
This paper extends previous work by showing that groups with many non-conjugate homomorphisms into mapping class groups have actions on trees, revealing structural properties of such groups.
Contribution
It demonstrates, using new methods and an auxiliary result, that finitely generated groups with infinitely many homomorphisms into mapping class groups virtually act on trees.
Findings
Finitely generated groups with infinitely many homomorphisms act on $ ext{R}$-trees.
Finitely presented groups with such homomorphisms act on simplicial trees.
Utilizes methods from previous work and an auxiliary result by Bestvina-Bromberg-Fujiwara.
Abstract
This is an addendum to arXiv: 0810.5376. We show, using our methods and an auxiliary result of Bestvina-Bromberg-Fujiwara, that a finitely generated group with infinitely many pairwise non-conjugate homomorphisms to a mapping class group virtually acts non-trivially on an -tree, and, if it is finitely presented, it virtually acts non-trivially on a simplicial tree
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Taxonomy
TopicsGeometric and Algebraic Topology · Finite Group Theory Research · Advanced Algebra and Geometry
