Department of Mathematics
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Generating the twist subgroup by involutions
Altunöz, Tülin; Pamuk, Mehmetcik; Yildiz, Oguz (2020-01-01)
© World Scientific Publishing CompanyFor 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 consid...
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...
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; Repovs, Dusan; 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 ...
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...
Homotopy self-equivalences of 4-manifolds with pi(1)-free second homotopy
Pamuk, Mehmetcik (Mathematical Society of Japan (Project Euclid), 2011-07-01)
We calculate the group of homotopy classes of homotopy self-equivalences of 4-manifolds with pi(1)-free second homotopy.
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