On the arc and curve complex of a surface

Download

index.pdf

Date

2010-05-01

Author

Korkmaz, Mustafa

Metadata

Show full item record

This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Item Usage Stats

265
views

83
downloads

We study the arc and curve complex AC(S) of an oriented connected surface S of finite type with punctures. We show that if the surface is not a sphere with one, two or three punctures nor a torus with one puncture, then the simplicial automorphism group of AC(S) coincides with the natural image of the extended mapping class group of S in that group. We also show that for any vertex of AC(S), the combinatorial structure of the link of that vertex characterizes the type of a curve or of an arc in S that represents that vertex. We also give a proof of the fact if S is not a sphere with at most three punctures, then the natural embedding of the curve complex of S in AC (S) is a quasi-isometry. The last result, at least under some slightly more restrictive conditions on S. was already known. As a corollary, AC (S) is Gromov-hyperbolic.

Subject Keywords

General Mathematics

URI

https://hdl.handle.net/11511/34500

Journal

MATHEMATICAL PROCEEDINGS OF THE CAMBRIDGE PHILOSOPHICAL SOCIETY

DOI

https://doi.org/10.1017/s0305004109990387

Collections

Department of Mathematics, Article

Suggestions

OpenMETU
Core

On entire rational maps of real surfaces Ozan, Yıldıray (The Korean Mathematical Society, 2002-01-01) In this paper, we define for a component X-0 of a nonsingular compact real algebraic surface X the complex genus of X-0, denoted by g(C)(X-0), and use this to prove the nonexistence of nonzero degree entire rational maps f : X-0 --> Y provided that g(C)(Y) > g(C)(X-0), analogously to the topological category. We construct connected real surfaces of arbitrary topological genus with zero complex genus.
On symplectic quotients of K3 surfaces Cinkir, Z; Onsiper, H (Elsevier BV, 2000-12-18) In this note, we construct generalized Shioda-Inose structures on K3 surfaces using cyclic covers and almost functoriality of Shioda-Inose structures with respect to normal subgroups of a given group of symplectic automorphisms.
On the Krall-type polynomials on q-quadratic lattices Alvarez-Nodarse, R.; Adiguzel, R. Sevinik (Elsevier BV, 2011-08-01) In this paper, we study the Krall-type polynomials on non-uniform lattices. For these polynomials the second order linear difference equation, q-basic series representation and three-term recurrence relations are obtained. In particular, the q-Racah-Krall polynomials obtained via the addition of two mass points to the weight function of the non-standard q-Racah polynomials at the ends of the interval of orthogonality are considered in detail. Some important limit cases are also discussed. (C) 2011 Royal Net...
On the moduli of surfaces admitting genus 2 fibrations Onsiper, H; Tekinel, C (Springer Science and Business Media LLC, 2002-12-01) We investigate the structure of the components of the moduli space Of Surfaces of general type, which parametrize surfaces admitting nonsmooth genus 2 fibrations of nonalbanese type, over curves of genus g(b) greater than or equal to 2.
NONCOMMUTATIVE MACKEY THEOREM Dosi, Anar (World Scientific Pub Co Pte Lt, 2011-04-01) In this note we investigate quantizations of the weak topology associated with a pair of dual linear spaces. We prove that the weak topology admits only one quantization called the weak quantum topology, and that weakly matrix bounded sets are precisely the min-bounded sets with respect to any polynormed topology compatible with the given duality. The technique of this paper allows us to obtain an operator space proof of the noncommutative bipolar theorem.

Citation Formats

M. Korkmaz, “On the arc and curve complex of a surface,” MATHEMATICAL PROCEEDINGS OF THE CAMBRIDGE PHILOSOPHICAL SOCIETY, pp. 473–483, 2010, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/34500.