2025/12/19 by Celal Can Bellek, Bellek, Celal Can · 1 citation
Mathematics · #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #Finite Group Theory Research
paper · doi:10.48550/arxiv.2512.17457
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.