On Nielsen equivalence classes of two-elements generators of mapping class groups

2025/05/12 by Susumu Hirose, Naoyuki Monden, Hirose, Susumu +1
Mathematics · #FOS: Mathematics #Geometric Topology (math.GT) #Group Theory (math.GR)

paper · doi:10.48550/arxiv.2505.07284

Abstract

We show that there are infinitely many Nielsen equivalence classes of the mapping class group of a closed oriented surface of genus at least eight.

Citations

• Die Gruppe der Abbildungsklassen: Das arithmetische Feld auf Flächen
• A group with an infinite number of Nielsen inequivalent one-relator presentations
• On free products with amalgamation of two infinite cyclic groups
• The mapping class group is generated by two commutators
• Generating pairs of 2-bridge knot groups

Related

• Generating the mapping class group by torsion elements of small order
• Generating mapping class group by two torsion elements
• Generating Extended Mapping Class Groups with Two Periodic Elements
• Mapping class group is generated by three involutions
• On generating mapping class groups by pseudo-Anosov elements