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Algorithms detecting stability and Morseness for finitely generated groups

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Heejoung Kim (UIUC)

For a word-hyperbolic group G, the notion of quasiconvexity is independent on the choice of a generating set and a quasiconvex subgroup of G is quasi-isometrically embedded in G. In 1994 Kapovich provided a partial algorithm which, on input a finite set S of G, halts if S generates a quasiconvex subgroup of G and runs forever otherwise.
However, beyond word-hyperbolic groups, the notion of quasiconveixty is not as useful.
For a finitely generated group, there are two recent generalizations of the notion of a quasiconvex subgroup of a word-hyperbolic group, a ``stable'' subgroup and a ``Morse'' subgroup.
In this talk, we will discuss various detection and decidability algorithms for stability and Morseness of a finitely generated subgroup of mapping class groups, right-angled Artin groups, toral relatively hyperbolic groups.