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Introduction Complex C Aut C

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75 pages
Introduction Complex C Aut(C) Thompson's group T is the automorphism group of a cellular complex associated to a surface of infinite type Ariadna Fossas (joint work with Maxime Nguyen) Universite Joseph Fourier Universitat Politecnica de Catalunya Fribourg, 12/10/2011 Ariadna Fossas T as automorphism group

  • only consider homeomorphisms

  • cellular complex associated

  • introduction complex

  • extended mapping class

  • orientable surface

  • orientation-preserving automorphisms

  • surface ?0


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Thompson’s groupTis the automorphism group of a cellular complex associated to a surface of infinite type
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Fribourg, 12/10/2011
Ariadna Fossas (joint work with Maxime Nguyen)
Universite´JosephFourier UniversitatPolite`cnicadeCatalunya
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Funar-Kapoudjan, 2004. There exists a planar surfaceΣof infinite type which has Thompson’s groupTasasymptotic mapping class group.
Results and motivation Goal of the talk
The surfaceΣis half of the surfaceΣ0. , The complexCis a restriction ofCp0,). The wordasymptoticmeans that we only consider homeomorphismsfthat are ’essentially trivial’ outside a compact subsurfaceSand its imagef(S).
F.-Nguyen, 2011 There exists a cellular complexCsuch that Aut+(C)' T, where Aut+=subgroup of orientation-preserving automorphisms.
Where does the complexCcome from?
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duroioctntItuAC)C(moCnxelp
Results and motivation Goal of the talk
Funar-Kapoudjan, 2004. There exists a planar surfaceΣof infinite type which has Thompson’s groupTasasymptotic mapping class group.
Where does the complexCcome from?
F.-Nguyen, 2011 There exists a cellular complexCsuch that Aut+(C)' T, where Aut+=subgroup of orientation-preserving automorphisms.
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The surfaceΣis half of the surfaceΣ0,. The complexCis a restriction ofCp0,). The wordasymptoticmeans that we only consider homeomorphismsfthat are ’essentially trivial’ outside a compact subsurfaceSand its imagef(S).
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Results and motivation Goal of the talk
The surfaceΣis half of the surfaceΣ0,. The complexCis a restriction ofCp0,). The wordasymptoticmeans that we only consider homeomorphismsfthat are ’essentially trivial’ outside a compact subsurfaceSand its imagef(S).
Where does the complexCcome from?
Funar-Kapoudjan, 2004. There exists a planar surfaceΣof infinite type which has Thompson’s groupTasasymptotic mapping class group.
F.-Nguyen, 2011 There exists a cellular complexCsuch that Aut+(C)' T, where Aut+=subgroup of orientation-preserving automorphisms.
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Margalit, 2004 MCGg,n)'Aut(Cp), unlessg= 0andn4, org= 1and n2, org= 2andn= 0.
Σg,n connected, orientable surface of genus: compact,gwith nboundary components. MCG(Σ) =Homeo(Σ)/Homeo0(Σ): extended mapping class group ofΣ. Cc complex of: curveΣg,n. Cp complex of: pantsΣg,n.
Ivanov-Korkmaz, 1997 MCGg,n)'Aut(Cc), unlessg= 0andn4, org= 1and n2, org= 2andn= 0.
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Results and motivation The compact case: selection of known results
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Σg,n: compact, connected, orientable surface of genusgwith nboundary components. MCG(Σ) =Homeo(Σ)/Homeo0(Σ) mapping class: extended group ofΣ. Cc: curve complex ofΣg,n. Cp: pants complex ofΣg,n.
Ivanov-Korkmaz, 1997 MCGg,n)'Aut(Cc), unlessg= 0andn4, org= 1and n2, org= 2andn= 0.
Results and motivation The compact case: selection of known results
Margalit, 2004 MCGg,n)'Aut(Cp), unlessg= 0andn4, org= 1and n2, org= 2andn= 0.
pouomotuasargmsihpriadnArsasTaFos
Results and motivation The compact case: selection of known results
Σg,n connected, orientable surface of genus: compact,gwith nboundary components. MCG(Σ) =Homeo(Σ)/Homeo0(Σ): extended mapping class group ofΣ. Cc: curve complex ofΣg n. , Cp complex of: pantsΣg,n.
Margalit, 2004 MCGg,n)'Aut(Cp), unlessg= 0andn4, org= 1and n2, org= 2andn= 0.
Ivanov-Korkmaz, 1997 MCGg,n)'Aut(Cc), unlessg= 0andn4, org= 1and n2, org= 2andn= 0.
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