Multitwists in big mapping class groups
George Domat, Federica Fanoni, Sebastian Hensel
TL;DR
This paper demonstrates that for infinite-type surfaces, the closure of the compactly supported mapping class group cannot be generated solely by multitwists, highlighting a fundamental difference from finite-type cases.
Contribution
It establishes that multitwists do not generate the entire closure of the compactly supported mapping class group in infinite-type surfaces, revealing new structural insights.
Findings
Multitwists do not generate the closure of the compactly supported mapping class group.
The structure of infinite-type surface mapping class groups differs from finite-type cases.
The result impacts understanding of the algebraic structure of infinite-type surface groups.
Abstract
We show that the closure of the compactly supported mapping class group of an infinite-type surface is not generated by the collection of multitwists (i.e. products of powers of twists about disjoint non-accumulating curves).
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Taxonomy
TopicsGeometric and Algebraic Topology · Algebraic Geometry and Number Theory · Homotopy and Cohomology in Algebraic Topology