2023/08/17 by Nick Salter, Salter, Nick, Abdoul Karim Sane +1
Computer Science · Mathematics · #Digital Image Processing Techniques #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Topological and Geometric Data Analysis
paper · pdf · doi:10.48550/arxiv.2308.09165
openalex publication_date 2023/08/17 · openalex created_date 2023/08/22 · openalex updated_date 2026/07/28
A unicellular collection on a surface is a collection of curves whose complement is a single disk. There is a natural surgery operation on unicellular collections, endowing the set of such with a graph structure where the edge relation is given by surgery. Here we determine the connected components of this graph, showing that they are enumerated by a certain homological "surgery invariant". Our approach is group-theoretic and proceeds by understanding the action of the mapping class group on unicellular collections. In the course of our arguments, we determine simple generating sets for the stabilizer in the mapping class group of a mod-2 homology class, which may be of independent interest.