Tulin Altunoz

activity

20192026

most citedThe Number of Singular Fibers in Hyperelliptic Lefschetz Fibrations

3 citations · 3 across the 13 of their papers we have counts for

collaborators

15 papers

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

Constructing Lefschetz Fibrations with Arbitrary Slope

Tulin Altunoz, Adalet Cengel

We prove that for any rational number $r \in (2, 8)$ , there exists a genus- $g$ Lefschetz fibration over the two-sphere with large enough genus- $g$ having the slope is $r$ .

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.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.GT2021

Small Lefschetz Fibrations on Simply-Connected $4$ -Manifolds

Tulin Altunoz

We consider simply-connected $4$ -manifolds admitting Lefschetz fibrations over the $2$ -sphere. We explicitly construct nonhyperelliptic and hyperelliptic Lefschetz fibrations of ge…

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.GT2020★ 3 cited

The Number of Singular Fibers in Hyperelliptic Lefschetz Fibrations

Tulin Altunoz

We consider complex surfaces, viewed as smooth $4$ -dimensional manifolds, that admit hyperelliptic Lefschetz fibrations over the $2$ -sphere. In this paper, we show that the minimal…

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

Genus- $3$ Lefschetz Fibrations and Exotic $4$ -Manifolds with $b_{2}^{+} = 3$

Tulin Altunoz

We explicitly construct a genus- $3$ Lefschetz fibration over $S^{2}$ whose total space is $T^{2} \times S^{2} #6 C P^{2}$ using the mo…

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…

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

Constructing Lefschetz Fibrations with Arbitrary Slope

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

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

On the Torsion Generators of the Mapping Class Groups

Involution Generators of the Big Mapping Class Group

Small Lefschetz Fibrations on Simply-Connected 4-Manifolds

The Twist Subgroup is generated by two elements

The Number of Singular Fibers in Hyperelliptic Lefschetz Fibrations

Generating the Extended Mapping Class Group by Three Involutions

Genus-3 Lefschetz Fibrations and Exotic 4-Manifolds with b2+​=3

Torsion Generators of the Twist Subgroup

Generating the Twist Subgroup by Involutions

Small Lefschetz Fibrations on Simply-Connected $4$ -Manifolds

Genus- $3$ Lefschetz Fibrations and Exotic $4$ -Manifolds with $b_{2}^{+} = 3$