2020/10/25 by Beth Branman, Branman, B.
Computer Science · Mathematics · #57M07 (primary) 37E30 (secondary) #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Group Theory (math.GR) #Homotopy and Cohomology in Algebraic Topology #Topological and Geometric Data Analysis
paper · pdf · doi:10.48550/arxiv.2010.13169
openalex publication_date 2020/10/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study the pants complex of surfaces of infinite type. When S is a surface of infinite type, the usual definition of the pants graph P(S) yields a graph with infinitely many connected-components. In the first part of our paper, we study this disconnected graph. In particular, we show that the extended mapping class group Mod(S) is isomorphic to a proper subgroup of Aut(P), in contrast to the finite-type case where Mod(S)≅ Aut(P(S)). In the second part of the paper, motivated by the Metaconjecture of Ivanov, we seek to endow P(S) with additional structure. To this end, we define a coarser topology on P(S) than the topology inherited from the graph structure. We show that our new space is path-connected, and that its automorphism group is isomorphic to Mod(S).