The geometry of flip graphs and mapping class groups
The space of topological decompositions into triangulations of a surface has a natural graph structure where two triangulations share an edge if they are related by a so-called flip. This space is a sort of combinatorial Teichmüller space and is quasi-isometric to the underlying mapping class group...
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| Main Authors: | , |
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| Format: | Article (Journal) |
| Language: | English |
| Published: |
2019, June 17
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| In: |
Transactions of the American Mathematical Society
Year: 2019, Volume: 372, Issue: 6, Pages: 3809-3844 |
| ISSN: | 1088-6850 |
| DOI: | 10.1090/tran/7356 |
| Online Access: | Verlag, Volltext: https://doi.org/10.1090/tran/7356 Verlag: https://www.ams.org/tran/2019-372-06/S0002-9947-2019-07356-7/ 
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| Author Notes: | Valentina Disarlo and Hugo Parlier |
| Summary: | The space of topological decompositions into triangulations of a surface has a natural graph structure where two triangulations share an edge if they are related by a so-called flip. This space is a sort of combinatorial Teichmüller space and is quasi-isometric to the underlying mapping class group. We study this space in two main directions. We first show that strata corresponding to triangulations containing a same multiarc are strongly convex within the whole space and use this result to deduce properties about the mapping class group. We then focus on the quotient of this space by the mapping class group to obtain a type of combinatorial moduli space. In particular, we are able to identity how the diameters of the resulting spaces grow in terms of the complexity of the underlying surfaces. |
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| Item Description: | Gesehen am 26.02.2020 |
| Physical Description: | Online Resource |
| ISSN: | 1088-6850 |
| DOI: | 10.1090/tran/7356 |