A Degree Theorem for the Space of Ribbon Graphs

zbMATH Open1312.57002arXiv1302.0554MaRDI QIDQ5174637

Bradley Forrest

Publication date: 18 February 2015

Abstract: This paper extends results of Hatcher and Vogtmann's work "Cerf Theory for Graphs" to ribbon graphs. Given an orientable, punctured and basepointed surface Sigma, we prove that the space of ribbon graphs that can be drawn in Sigma is filtered by simplicial complexes. The k-th simplicial complex is (k-1)-dimensional, (k-2)-connected and invariant under the action of the basepoint preserving mapping class group of Sigma.

Full work available at URL: https://arxiv.org/abs/1302.0554

zbMATH Keywords

mapping class groupsribbon graphs

Mathematics Subject Classification ID

Geometric group theory (20F65) Moduli of Riemann surfaces, Teichmüller theory (complex-analytic aspects in several variables) (32G15) Relations of low-dimensional topology with graph theory (57M15)

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