Big mapping class groups fail the Tits alternative

Abstract: Let \(S\) be a surface with infinitely many punctures, or infinitely many handles, or containing a disk minus Cantor set. (This accounts for almost all infinite-type surfaces.) Then the mapping class group of S fails to satisfy the Tits alternative. Namely, we construct a finitely generated subgroup which is not virtually solvable and contains no free group of rank greater than one. The Grigorchuk group is a key element in the construction.

algebraic topologydifferential geometrydynamical systemsgroup theorygeometric topologysymplectic geometry

Audience: researchers in the topic

Geometry and topology online

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