Work

Homeomorphism groups of telescoping $2$-manifolds are strongly distorted

Year: 2025

Type: article

Abstract: Building on the work of Mann and Rafi, we introduce an expanded definition of a telescoping 2 -manifold and proceed to study the homeomorphism group of a telescoping 2 -manifold. Our main result shows that it is strongly distorted. We then give a simple description of its commutator subgroup, which is index one, two, or four depending on the topology of the manifold. Moreover, we show its commutator subgroup is uniformly perfect with commutator width at most two, and we give a family of uniform normal generators for its commutator subgroup. As a consequence of the latter result, we show that for an (orientable) telescoping 2 -manifold, every (orientation-preserving) homeomorphism can be expressed as a product of at most 17 conjugate involutions. Finally, we provide analogous statements for mapping class groups.

Source: Groups Geometry and Dynamics

DOI: 10.4171/ggd/867

Author: Nicholas G. Vlamis

Institutions: Queens College, CUNY, The Graduate Center, CUNY

Language: English

Topic: Geometric and Algebraic Topology

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: diamond

Funders: National Science Foundation, City University of New York

Award: LEAPS-MPS: Topological Symmetries of Non-Compact Riemann Surfaces