Department of Mathematics
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Browsing Department of Mathematics by Author "Atalan Ozan, Ferihe"
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Item AUTOMORPHISMS OF THE GRAPH OF CURVES(2017-05-02) Elamin, Amel Omar; Atalan Ozan, FeriheIn this thesis, we study the automorphisms of a certain graph of nonseparating curves and automorphisms of complexes of two-sided curves on surfaces. In Chapter 3, we deal with the work of P. S. Schaller on mapping class groups of hyperbolic surfaces and automorphism groups of graphs for orientable surfaces of genus g ≥ 1 with n punctures. More precisely, it is shown that the automorphism group of the certain graph is isomorphic to the extended mapping class group of the orientable surface proved by Schaller. In the last chapter of this thesis, we study the automorphisms of the complexes of two-sided simple closed curves on nonorientable surfaces of genus g with n holes.Item CONNECTEDNESS OF THE CUT-SYSTEM COMPLEX ON SURFACES(2017-05-02) Ali, Fatema; Atalan Ozan, FeriheLet M be a compact, connected, orientable or nonorientable surface of genus g ≥ 1 with n boundary components. In this thesis, we study connectedness of cut-system complex of M. More precisely, in Chapter 3, we study the work of Wajnryb on the connectedness of the cut-system complex of an orientable surface. In the last chapter, we prove that the cut-system complex of a nonorientable surface is connected.