Morse theory and conjugacy classes of finite subgroups

Details Morse theory and conjugacy classes of finite subgroups Morse theory and conjugacy classes of finite subgroups

2007-09-24

arxiv.org/abs/0709.3802v1

Mathematics

Group Theory

10 pages, 4 figures

Scientific paper

We construct a CAT(0) group containing a finitely presented subgroup with infinitely many conjugacy classes of finite-order elements. Unlike previous examples (which were based on right-angled Artin groups) our ambient CAT(0) group does not contain any rank 3 free abelian subgroups. We also construct examples of groups of type F_n inside mapping class groups, Aut(F), and Out(F) which have infinitely many conjugacy classes of finite-order elements.

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