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20192025

most citedGenerating the mapping class group by three involutions

2 citations · 4 across the 11 of their papers we have counts for

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13 papers · 1 filter

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.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.GT2020★ 2 cited

Generating mapping class group by two torsion elements

Oguz Yildiz

We prove that the mapping class group of a closed connected orientable surface of genus $g$ is generated by two elements of order $g$ for $g \geq 6$ . Moreover, for $g \geq 7$ we foun…

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★ 2 cited

Generating the mapping class group by three involutions

Oguz Yildiz

We prove that the mapping class group of a closed connected orientable surface of genus $g$ is generated by three involutions for $g \geq 6$ .

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…