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Mustafa Korkmaz

Department of Mathematics
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Finite rigid sets in curve complexes of nonorientable surfaces
Ilbira, Sabahattin; Korkmaz, Mustafa (Springer Science and Business Media LLC, 2020-06-01)
A rigid set in a curve complex of a surface is a subcomplex such that every locally injective simplicial map from the set into the curve complex is induced by a homeomorphism of the surface. In this paper, we find finite r...
Mapping class group is generated by three involutions
Korkmaz, Mustafa (2020-01-01)
We prove that the mapping class group of a closed connected orientable surface of genus at least eight is generated by three involutions.
Small Lefschetz fibrations and exotic 4-manifolds
Baykur, R. Inanc; Korkmaz, Mustafa (Springer Science and Business Media LLC, 2017-04-01)
We explicitly construct genus-2 Lefschetz fibrations whose total spaces are minimal symplectic 4-manifolds homeomorphic to complex rational surfaces CP2#pCP (CP) over bar (2) for P = 7,8,9, and to 3CP(2)#qCP (CP) over bar ...
Arbitrarily Long Factorizations in Mapping Class Groups
DALYAN, ELİF; Korkmaz, Mustafa; Pamuk, Mehmetcik (2015-01-01)
On a compact oriented surface of genus g with n= 1 boundary components, d1, d2,..., dn, we consider positive factorizations of the boundary multitwist td1 td2 tdn, where tdi is the positive Dehn twist about the boundary di...
Automorphisms of curve complexes on nonorientable surfaces
Atalan, Ferihe; Korkmaz, Mustafa (2014-01-01)
For a compact connected nonorientable surface N of genus g with n boundary components, we prove that the natural map from the mapping class group of N to the automorphism group of the curve complex of N is an isomorphism p...
Baykur, R. Inanc; Korkmaz, Mustafa; Monden, Naoyuki (2013-11-01)
We investigate the possible self-intersection numbers for sections of surface bundles and Lefschetz fibrations over surfaces. When the fiber genus g and the base genus h are positive, we prove that the adjunction bound 2h-...
Korkmaz, Mustafa; Papadopoulos, Athanase (2012-01-01)
We study the ideal triangulation graph T(S) of an oriented punctured surface S of finite type. We show that if S is not the sphere with at most three punctures or the torus with one puncture, then the natural map from the ...
On the arc and curve complex of a surface
Korkmaz, Mustafa; Papadopoulos, Athanase (Cambridge University Press (CUP), 2010-05-01)
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 th...
Number of pseudo-Anosov elements in the mapping class group of a four-holed sphere
Atalan, Ferihe; Korkmaz, Mustafa (2010-01-01)
We compute the growth series and the growth functions of reducible and pseudo-Anosov elements of the pure mapping class group of the sphere with four holes with respect to a certain generating set We prove that the ratio o...
Lefschetz Fibrations and an Invariant of Finitely Presented Groups
Korkmaz, Mustafa (Oxford University Press (OUP), 2009-01-01)
Every finitely presented group is the fundamental group of the total space of a Lefschetz fibration. This follows from results of Gompf and Donaldson, and was also proved by Amoros-Bogomolov-Katzarkov-Pantev. We give anoth...