The geometry of flip graphs and mapping class groups

• Verfasst von: Disarlo, Valentina [VerfasserIn]
• Verfasst von: Parlier, Hugo [VerfasserIn]
• Titel: The geometry of flip graphs and mapping class groups
• Verf.angabe: Valentina Disarlo and Hugo Parlier
• E-Jahr: 2019
• Jahr: 2019, June 17
• Umfang: 36 S.
• Fussnoten: Gesehen am 26.02.2020
• Titel Quelle: Enthalten in: American Mathematical SocietyTransactions of the American Mathematical Society
• Ort Quelle: Providence, RI : Soc., 1900
• Jahr Quelle: 2019
• Band/Heft Quelle: 372(2019), 6, Seite 3809-3844
• ISSN Quelle: 1088-6850
• DOI: doi:10.1090/tran/7356
• Datenträger: Online-Ressource
• Sprache: eng
• Sach-SW: combinatorial moduli spaces
• Sach-SW: Flip graphs
• Sach-SW: mapping class groups
• Sach-SW: triangulations of surfaces
• K10plus-PPN: 1691063509

Abstract

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.