Unicellular maps and filtrations of the mapping class group

2020/06/29 by Abdoul Karim Sane, Sane, Abdoul Karim
Mathematics · #Combinatorics (math.CO) #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #Mathematical Dynamics and Fractals

paper · pdf · doi:10.48550/arxiv.2006.15880

openalex publication_date 2020/06/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This article first answers to questions about connectedness of a new family of graphs on unicellular maps. Answering these questions goes through a description of the mapping class group as surgeries on unicellular maps. We also show how unicellular maps encode subgroups of the mapping group and provide filtrations of the mapping class group. These facts add a layer on the ubiquitous character of unicellular maps.

Citations

• A finite set of generators for the homeotopy group of a 2-manifold

Related

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• Connected components of the topological surgery graph of a unicellular collection
• Fifteen problems about the mapping class groups
• Quotients of mapping class groups from Out(F_n)
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