scholarly journals Automorphisms of curve complexes on nonorientable surfaces

2014 ◽  
Vol 8 (1) ◽  
pp. 39-68 ◽  
Author(s):  
Ferihe Atalan ◽  
Mustafa Korkmaz
Keyword(s):  
Nonorientable Surfaces ◽  
Curve Complexes

scholarly journals Finite rigid sets in curve complexes of nonorientable surfaces

2019 ◽  
Vol 206 (1) ◽  
pp. 83-103 ◽  
Author(s):  
Sabahattin Ilbira ◽  
Mustafa Korkmaz
Keyword(s):  
Nonorientable Surfaces ◽  
Curve Complexes

scholarly journals Exhausting curve complexes by finite rigid sets on nonorientable surfaces

2022 ◽  
pp. 1-29
Author(s):  
Elmas Irmak
Keyword(s):  
Curve Complex ◽  
Nonorientable Surface ◽  
Nonorientable Surfaces ◽  
Genus Formula ◽  
Curve Complexes

Let [Formula: see text] be a compact, connected, nonorientable surface of genus [Formula: see text] with [Formula: see text] boundary components. Let [Formula: see text] be the curve complex of [Formula: see text]. We prove that if [Formula: see text] or [Formula: see text], then there is an exhaustion of [Formula: see text] by a sequence of finite rigid sets. This improves the author’s result on exhaustion of [Formula: see text] by a sequence of finite superrigid sets.

scholarly journals Exhausting curve complexes by finite rigid sets

2016 ◽  
Vol 282 (2) ◽  
pp. 257-283 ◽  
Author(s):  
Javier Aramayona ◽  
Christopher Leininger
Keyword(s):  
Curve Complexes

scholarly journals Bordifications of hyperplane arrangements and their curve complexes

2021 ◽  
Vol 14 (2) ◽  
pp. 419-459
Author(s):  
Michael W. Davis ◽  
Jingyin Huang
Keyword(s):  
Hyperplane Arrangements ◽  
Curve Complexes

scholarly journals Existence of minimal flows on nonorientable surfaces

2017 ◽  
Vol 37 (8) ◽  
pp. 4191-4211
Author(s):  
José Ginés Espín Buendía ◽  
◽  
Daniel Peralta-salas ◽  
Gabriel Soler López ◽  
◽  
...  
Keyword(s):  
Nonorientable Surfaces

scholarly journals Some results on Teichmüller spaces of Klein surfaces

1997 ◽  
Vol 39 (1) ◽  
pp. 65-76
Author(s):  
Pablo Arés Gastesi
Keyword(s):  
Riemann Surfaces ◽  
Riemann Sphere ◽  
Topological Type ◽  
Uniformization Theorem ◽  
Teichmüller Spaces ◽  
Teichmuller Spaces ◽  
Simply Connected Domain ◽  
Nonorientable Surfaces ◽  
Simply Connected ◽  
Orientable Surfaces

The deformation theory of nonorientable surfaces deals with the problem of studying parameter spaces for the different dianalytic structures that a surface can have. It is an extension of the classical theory of Teichmüller spaces of Riemann surfaces, and as such, it is quite rich. In this paper we study some basic properties of the Teichmüller spaces of non-orientable surfaces, whose parallels in the orientable situation are well known. More precisely, we prove an uniformization theorem, similar to the case of Riemann surfaces, which shows that a non-orientable compact surface can be represented as the quotient of a simply connected domain of the Riemann sphere, by a discrete group of Möbius and anti-Möbius transformation (mappings whose conjugates are Mobius transformations). This uniformization result allows us to give explicit examples of Teichmüller spaces of non-orientable surfaces, as subsets of deformation spaces of orientable surfaces. We also prove two isomorphism theorems: in the first place, we show that the Teichmüller spaces of surfaces of different topological type are not, in general, equivalent. We then show that, if the topological type is preserved, but the signature changes, then the deformations spaces are isomorphic. These are generalizations of the Patterson and Bers-Greenberg theorems for Teichmüller spaces of Riemann surfaces, respectively.

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