Department of Mathematics
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Generating the Mapping Class Group of a Nonorientable Surface by Two Elements or by Three Involutions
Altunöz, Tülin; Pamuk, Mehmetcik; Yildiz, Oguz (2022-01-01)
We prove that, for g≥ 19 the mapping class group of a nonorientable surface of genus g, Mod (Ng) , can be generated by two elements, one of which is of order g. We also prove that for g≥ 26 , Mod (Ng) can be generated by t...
Generating the twist subgroup by involutions
Altunöz, Tülin; Pamuk, Mehmetcik; Yildiz, Oguz (2020-01-01)
For a nonorientable surface, the twist subgroup is an index 2 subgroup of the mapping class group generated by Dehn twists about two-sided simple closed curves. In this paper, we consider involution generators of the twist...
Decomposing perfect discrete Morse functions on connected sum of 3-manifolds
Kosta, Neza Mramor; Pamuk, Mehmetcik; Varli, Hanife (2019-06-15)
In this paper, we show that if a closed, connected, oriented 3-manifold M = M-1 # M-2 admits a perfect discrete Morse function, then one can decompose this function as perfect discrete Morse functions on M-1 and M-2. We al...
Integral laminations on nonorientable surfaces
Oyku Yurttas, Syed; Pamuk, Mehmetcik (2018-01-01)
We describe triangle coordinates for integral laminations on a nonorientable surface N-k,N-n of genus kwithn punctures and one boundary component, and we give an explicit bijection from the set of integral laminations on N...
Perfect Discrete Morse Functions On Connected Sums
Pamuk, Mehmetcik (2017-07-01)
In this talk, we study perfect discrete Morse functions on closed oriented n-dimensional manifolds. First, we show how to compose such functions on connected sums of manifolds. Then we discuss how to decompose such functio...
A note on the generalized Matsumoto relation
DALYAN, ELİF; Medetogullari, Elif; Pamuk, Mehmetcik (2017-01-01)
We give an elementary proof of a relation, first discovered in its full generality by Korkmaz, in the mapping class group of a closed orientable surface. Our proof uses only the well-known relations between Dehn twists.
Homotopy classification of PD4 complexes
Pamuk, Mehmetcik; Hegenbarth, Friedrich (2015-07-17)
We define an order relation among oriented -complexes. We show that with respect to this relation, two -complexes over the same complex are homotopy equivalent if and only if there is an isometry between the second homolog...
s-Cobordism Classification of 4-Manifolds Through the Group of Homotopy Self-equivalences
Hegenbarth, Friedrich; Pamuk, Mehmetcik; Repovs, Dusan (2015-07-01)
The aim of this paper is to give an s-cobordism classification of topological 4 manifolds in terms of the standard invariants using the group of homotopy self-equivalences. Hambleton and Kreck constructed a braid to study ...
Nonsimply connected 4 manifolds
Pamuk, Mehmetcik (null; 2015-01-10)
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...
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