Mehmetcik Pamuk

activity

20092026

P D_{4}

-complexes relative an order relation

4 citations · 8 across the 23 of their papers we have counts for

collaborators

28 papers

math.GT2026

Homotopy Self-Equivalences of $R P^{2} \times S^{2}$ and a Braid for non-orientable $4$ -Manifolds

Mehmetcik Pamuk

We compute the group of based homotopy classes of self-homotopy equivalences of the non-orientable $4$ -manifold $\RP^2\times S^2$. It is an elementary abelian $2$ -group of rank $5$ …

math.AT2026

Homotopy Self-Equivalences of Manifolds

Mehmetcik Pamuk

Hambleton and Kreck described the group of based homotopy self-equivalences of a closed oriented $4$ -manifold by a commutative braid of exact sequences built from bordism groups an…

math.AT2026

Component-Perfect Multidimensional Discrete Morse Functions

Mehmetcik Pamuk, Hanife Varlı

We introduce the concept of component-perfect multidimensional discrete Morse (MDM) functions on finite regular CW complexes. While perfect discrete Morse functions in the classica…

math.GT2026

Small Sets of Generators for Handlebody Groups

Tülin Altunöz, Celal Can Bellek, Emir Gül +2

Wajnryb gave a finite presentation of the handlebody group $M (V_{g})$ and showed that it is generated by five elements for $g \geq 2$ . Using his relations, we show that $\ma…

math.GT2026

Small Torsion Topological Generators for Big Mapping Class Groups

Tülin Altunöz, Celal Can Bellek, Emir Gül +2

Let $S (n)$ , for $n \in N$ , be the infinite-type surface of infinite genus with $n$ ends, each accumulated by genus. Although the mapping class groups of these surfaces are…

math.GT2025

Small Sets of Topological Generators for Big Mapping Class Groups

Tülin Altunöz, Celal Can Bellek, Emir Gül +2

Let $S (n)$ be the infinite-type surface with infinite genus and $n \in N$ ends, all of which are accumulated by genus. The mapping class group of this surface, $\mathrm{Ma…

math.GT2025

Minimal Generation of Mapping Class Groups: A Survey of the Orientable Case

Tulin Altunoz, Mehmetcik Pamuk, Oguz Yildiz

The mapping class group of an orientable surface, which records its symmetries up to isotopy, plays a central role in low-dimensional topology. This chapter explores the foundation…

math.GT2025

Minimal Generation of Mapping Class Groups: A Survey of the Nonorientable Case

Tulin Altunoz, Mehmetcik Pamuk, Oguz Yildiz

This chapter provides a comprehensive survey of foundational results and recent advances concerning minimal generating sets for the mapping class group of a nonorientable surface,…

math.AT2024

A Closed Formula for the Interleaving Distance of Rectangle Persistence Modules

Mehmet Ali Batan, Claudia Landi, Mehmetcik Pamuk

We give formulas for calculating the interleaving distance between rectangle persistence modules that depend solely on the geometry of the underlying rectangles. Moreover, we exten…

math.GT2023

On the Torsion Generators of the Mapping Class Groups

Tulin Altunoz, Mehmetcik Pamuk, Oguz Yildiz

We study torsion generators for the (extended) mapping class group or the extended mapping class group of a closed connected orientable surface of genus g. We show that for every g…

math.GT2023

Involution Generators of the Big Mapping Class Group

Tulin Altunoz, Mehmetcik Pamuk, Oguz Yildiz

Let S = S(n) denote the infinite surface with n ends, n \in N, accumulated by genus. For n \geq 6, we show that the mapping class group of S is topologically generated by five invo…

math.GT2022

On the involution generators of the mapping class group of a punctured surface

Tulin Altunoz, Mehmetcik Pamuk, Oguz Yildiz

Let Mod(Sigma_{g, p}) denote the mapping class group of a connected orientable surface of genus g with p punctures. For every even integer p \geq 10 and g \geq 14, we prove that Mo…

math.GT2022

Generating the Level 2 Subgroup by Involutions

Tulin Altunoz, Naoyuki Monden, Mehmetcik Pamuk +1

We obtain a minimal generating set of involutions for the level 2 subgroup of the mapping class group of a closed nonorientable surface.

math.GT2021

Generating the Mapping Class Group of a Nonorientable Surface by Two Elements or By Three Involutions

Tulin Altunoz, Mehmetcik Pamuk, Oguz Yildiz

We prove that, for $g \geq 19$ the mapping class group of a nonorientable surface of genus $g$ , $Mod (N_{g})$ , can be generated by two elements, one of which is of order $g$ . W…

math.GT2021

The Twist Subgroup is generated by two elements

Tulin Altunoz, Mehmetcik Pamuk, Oguz Yildiz

We show that the twist subgroup $T_{g}$ of a nonorientable surface of genus $g$ can be generated by two elements for every odd $g \geq 27$ and even $g \geq 42$ . Using these gen…

math.AT2020

Contiguity Distance between Simplicial Maps

Ayse Borat, Mehmetcik Pamuk, Tane Vergili

We study properties of contiguity distance between simplicial maps. In particular, we show that simplicial versions of $L S$ -category and topological complexity are particular cases…

math.GT2020

Generating the Extended Mapping Class Group by Three Involutions

Tulin Altunoz, Mehmetcik Pamuk, Oguz Yildiz

We prove that the extended mapping class group, $Mo d^{*} (Σ_{g})$ , of a connected orientable surface of genus $g$ , can be generated by three involutions for $g \geq 5$ . In the pr…

math.GT2020

Torsion Generators of the Twist Subgroup

Tulin Altunoz, Mehmetcik Pamuk, Oguz Yildiz

We showed that the twist subgroup of the mapping class group of a closed connected nonorientable surface of genus $g \geq 13$ can be generated by two involutions and an element of or…

math.GT2019

Generating the Twist Subgroup by Involutions

Tulin Altunoz, Mehmetcik Pamuk, Oguz Yildiz

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 pape…

math.AT2019

Elementary Methods for Persistent Homotopy Groups

Henry Adams, Mehmet Ali Batan, Mehmetcik Pamuk +1

We study the foundational properties of persistent homotopy groups and develop elementary computational methods for their analysis. Our main theorems are persistent analogues of th…

math.AT2018★ 1 cited

Homological properties of persistent homology

Hanife Varlı, Yağmur Yılmaz, Mehmetcik Pamuk

We investigate to what extent persistent homology benefits from the properties of the usual homology theory.

math.AT2018

Decomposing Perfect Discrete Morse Functions on Connected Sums of 3-manifolds

Neza Mramor Kosta, Mehmetcik Pamuk, Hanife Varli

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…

math.GT2016

Integral laminations on non-orientable surfaces

S. Öykü Yurttaş, Mehmetcik Pamuk

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 bij…

math.GT2015★ 4 cited

Homotopy classification of $P D_{4}$ -complexes relative an order relation

Mehmetcik Pamuk, Friedrich Hegenbarth, Dušan Repovš

We define an order relation among oriented $P D_{4}$ -complexes. We show that with respect to this relation, two $P D_{4}$ -complexes over the same complex are homotopy equivalent if and o…

Homotopy Self-Equivalences of RP2×S2 and a Braid for non-orientable 4-Manifolds

Homotopy Self-Equivalences of Manifolds

Component-Perfect Multidimensional Discrete Morse Functions

Small Sets of Generators for Handlebody Groups

Small Torsion Topological Generators for Big Mapping Class Groups

Small Sets of Topological Generators for Big Mapping Class Groups

Minimal Generation of Mapping Class Groups: A Survey of the Orientable Case

Minimal Generation of Mapping Class Groups: A Survey of the Nonorientable Case

A Closed Formula for the Interleaving Distance of Rectangle Persistence Modules

On the Torsion Generators of the Mapping Class Groups

Involution Generators of the Big Mapping Class Group

On the involution generators of the mapping class group of a punctured surface

Generating the Level 2 Subgroup by Involutions

Generating the Mapping Class Group of a Nonorientable Surface by Two Elements or By Three Involutions

The Twist Subgroup is generated by two elements

Contiguity Distance between Simplicial Maps

Generating the Extended Mapping Class Group by Three Involutions

Torsion Generators of the Twist Subgroup

Generating the Twist Subgroup by Involutions

Elementary Methods for Persistent Homotopy Groups

Homological properties of persistent homology

Decomposing Perfect Discrete Morse Functions on Connected Sums of 3-manifolds

Integral laminations on non-orientable surfaces

Homotopy classification of PD4​-complexes relative an order relation

Homotopy Self-Equivalences of $R P^{2} \times S^{2}$ and a Braid for non-orientable $4$ -Manifolds

Homotopy classification of $P D_{4}$ -complexes relative an order relation