2025/12/19 by Tülin Altunöz, Altunöz, Tülin, Celal Can Bellek +7
Mathematics · #Geometric and Algebraic Topology #Algebraic Geometry and Number Theory #Homotopy and Cohomology in Algebraic Topology
paper · doi:10.48550/arxiv.2512.17465
Let S(n) be the infinite-type surface with infinite genus and n ∈ ℕ ends, all of which are accumulated by genus. The mapping class group of this surface, Map(S(n)), is a Polish group that is not countably generated, but it is countably topologically generated. This paper focuses on finding minimal sets of generators for Map(S(n)). We show that for n ≥ 8, Map(S(n)) is topologically generated by three elements, and for n ≥ 3, it is topologically generated by four elements. We also establish a generating set of two elements for the Loch Ness Monster surface S(1), and a generating set of three elements for the Jacob's Ladder surface S(2).