On powers of half-twists in M(0,2n)

2016/08/30 by Gregor Masbaum, Masbaum, Gregor
Computer Science · Mathematics · #20F38 #57M99 #57R56 #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #Quantum Algebra (math.QA) #math.GT #math.QA #msc:20F38 #msc:57M99 #msc:57R56 #semigroups and automata theory

paper · pdf · doi:10.48550/arxiv.1608.08449

5 pages. v2: Reference to S. P. Humphries added in the Introduction and in Remark 3.5

openalex publication_date 2016/08/30 · arxiv created 2016/10/14 · arxiv updated 2016/10/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We use elementary skein theory to prove a version of a result of Stylianakis who showed that under mild restrictions on m and n, the normal closure of the m-th power of a half-twist has infinite index in the mapping class group of a sphere with 2n punctures.

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