Introduction Complex C Aut C

Maxime Nguyen

Description

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

Sujets

• Nguy?n
• Orientability

Informations

• Publié par: pefav
• Nombre de lectures: 9
• Langue: English
• Poids de l'ouvrage: 1 Mo

Extrait

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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 surfaceΣ 0∞ . , The complexCis a restriction ofC p (Σ 0,∞ ). 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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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 surfaceΣ 0,∞ . The complexCis a restriction ofC p (Σ 0,∞ ). 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 surfaceΣ 0,∞ . The complexCis a restriction ofC p (Σ 0,∞ ). 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 MCG ∗ (Σ g,n )'Aut(C p ), unlessg= 0andn≤4, org= 1and n≤2, org= 2andn= 0.

Σ g,n  connected, orientable surface of genus: compact,gwith nboundary components. MCG ∗ (Σ) =Homeo(Σ)/Homeo 0 (Σ): extended mapping class group ofΣ. C c  complex of: curveΣ g,n . C p  complex of: pantsΣ g,n .

Ivanov-Korkmaz, 1997 MCG ∗ (Σ g,n )'Aut(C c ), unlessg= 0andn≤4, org= 1and n≤2, org= 2andn= 0.

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Results and motivation The compact case: selection of known results

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Σ g,n : compact, connected, orientable surface of genusgwith nboundary components. MCG ∗ (Σ) =Homeo(Σ)/Homeo 0 (Σ) mapping class: extended group ofΣ. C c : curve complex ofΣ g,n . C p : pants complex ofΣ g,n .

Ivanov-Korkmaz, 1997 MCG ∗ (Σ g,n )'Aut(C c ), unlessg= 0andn≤4, org= 1and n≤2, org= 2andn= 0.

Results and motivation The compact case: selection of known results

Margalit, 2004 MCG ∗ (Σ g,n )'Aut(C p ), unlessg= 0andn≤4, org= 1and n≤2, org= 2andn= 0.

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Results and motivation The compact case: selection of known results

Σ g,n  connected, orientable surface of genus: compact,gwith nboundary components. MCG ∗ (Σ) =Homeo(Σ)/Homeo 0 (Σ): extended mapping class group ofΣ. C c : curve complex ofΣ g n . , C p  complex of: pantsΣ g,n .

Margalit, 2004 MCG ∗ (Σ g,n )'Aut(C p ), unlessg= 0andn≤4, org= 1and n≤2, org= 2andn= 0.

Ivanov-Korkmaz, 1997 MCG ∗ (Σ g,n )'Aut(C c ), unlessg= 0andn≤4, org= 1and n≤2, org= 2andn= 0.

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