The mapping class group is generated by two commutators
R. Inanc Baykur, Mustafa Korkmaz
TL;DR
This paper proves that the mapping class group of a closed orientable surface can be generated by a small number of commutators, specifically two for genus at least five, and three for genus three or four.
Contribution
It establishes minimal generating sets for the mapping class group using only a few commutators, improving understanding of its algebraic structure.
Findings
Generated by two commutators for genus ≥ 5
Generated by three commutators for genus 3 or 4
Provides explicit bounds on the number of commutators needed
Abstract
We show that the mapping class group of any closed connected orientable surface of genus at least five is generated by only two commutators, and if the genus is three or four, by three commutators.
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