arXiv subjects
Publications and source records attributed to Mehmetcik Pamuk.
We study properties of contiguity distance between simplicial maps. In particular, we show that simplicial versions of $LS$-category and topological complexity are particular cases of this more general notion.
We showed that the twist subgroup of the mapping class group of a closed connected nonorientable surface of genus $g\geq13$ can be generated by two involutions and an element of order $g$ or $g-1$ depending on whether $g$ is odd or even respectively.
For a nonorientable surface, the twist subgroup is an index 2 subgroup of the mapping class group. It is generated by Dehn twists about two-sided simple closed curves. In this paper, we study involution generators of the twist subgroup. We give generating sets of involutions with the smallest number of elements our methods allow.
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 the group of homotopy self-equivalences of $4$-manifolds. Using this braid together with the modified surgery theory of Kreck, we give an $s$-cobordism classification for certain $4$-manifolds with fundamental group $π$, such that cd $π\leq 2$.
We investigate to what extent persistent homology benefits from the properties of the usual homology theory.
In this paper, we show that if a closed, connected, oriented 3-manifold M = M1#M2 admits a perfect discrete Morse function, then one can decompose this function as perfect discrete Morse functions on M_1 and M_2. We also give an explicit construction of a separating sphere on M corresponding to such a decomposition.
We describe triangle coordinates for integral laminations on a non-orientable surface $N_{k,n}$ of genus $k$ with $n$ punctures and one boundary component, and give an explicit bijection from the set of integral laminations on $N_{k,n}$ to $(\mathbb{Z}^{2(n+k-2)}\times \mathbb{Z}^k)\setminus \left\{0\right\}$.
We study perfect discrete Morse functions on closed oriented n-dimensional manifolds. We show how to compose such functions on connected sums of closed oriented manifolds and how to decompose on connected sums of closed oriented surfaces.
We define an order relation among oriented $PD_4$-complexes. We show that with respect to this relation, two $PD_4$-complexes over the same complex are homotopy equivalent if and only if there is an isometry between the second homology groups. We also consider minimal objects of this relation.
On a compact oriented surface of genus $g$ with $n\geq 1$ boundary components, $δ_1, δ_2,\ldots, δ_n$, we consider positive factorizations of the boundary multitwist $t_{δ_1} t_{δ_2} \cdots t_{δ_n}$, where $t_{δ_i}$ is the positive Dehn twist about the boundary $δ_i$. We prove that for $g\geq 3$, the boundary multitwist $t_{δ_1} t_{δ_2}$ can be written as a product of arbitrarily large number of positive Dehn twists about nonseparating simple closed curves, extending a recent result of Baykur and Van Horn-Morris, who proved this result for $g\geq 8$. This fact has immediate corollaries on the Euler characteristics of the Stein fillings of conctact three manifolds.
Let $T$ denote a binding component of an open book $(Σ, ϕ)$ compatible with a closed contact 3-manifold $(M, ξ)$. We describe an explicit open book $(Σ', ϕ')$ compatible with $(M, ζ)$, where $ζ$ is the contact structure obtained from $ξ$ by performing a full Lutz twist along $T$. Here, $(Σ', ϕ')$ is obtained from $(Σ, ϕ)$ by a \emph{local} modification near the binding.