Structure and Topological Generation of Big Mapping Class Groups
Celal Can Bellek

TL;DR
This paper explores the structure and generation properties of big mapping class groups associated with infinite-type surfaces, highlighting key differences from finite-type cases and summarizing recent foundational results.
Contribution
It provides a systematic overview of the structure and topological generation of big mapping class groups, emphasizing new insights and differences from classical finite-type surface groups.
Findings
Finite topological generation results for certain infinite-type surfaces
Clear exposition of structural differences from finite-type mapping class groups
Summary of foundational results in the field
Abstract
Big mapping class groups are the mapping class groups of infinite-type surfaces, that is, surfaces whose fundamental groups are not finitely generated. While mapping class groups of finite-type surfaces have been extensively studied, the theory of big mapping class groups is a recent and rapidly developing area of research. This thesis provides a systematic introduction to the structure and topological generation of big mapping class groups, emphasizing the key differences from the classical finite-type case. It presents a clear exposition of foundational results concerning their topological and algebraic structure, including known results on finite topological generation for a certain family of infinite-type surfaces.
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Taxonomy
TopicsGeometric and Algebraic Topology · Homotopy and Cohomology in Algebraic Topology · Finite Group Theory Research
