8 papers
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…
Small Sets of Generators for Handlebody Groups
Tülin Altunöz, Celal Can Bellek, Emir Gül +2
The mapping class group of a -dimensional handlebody of genus , denoted by , is a fundamental object of study in geometric topology. Building upon the initi…
Small Sets of Topological Generators for Big Mapping Class Groups
Tülin Altunöz, Celal Can Bellek, Emir Gül +2
Let be the infinite-type surface with infinite genus and ends, all of which are accumulated by genus. The mapping class group of this surface, $\mathrm{Ma…
Small Torsion Topological Generators for Big Mapping Class Groups
Tülin Altunöz, Celal Can Bellek, Emir Gül +2
Let , for , be the infinite-type surface of infinite genus with ends, each accumulated by genus. Although the mapping class groups of these surfaces are…
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…
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,…