2018/01/18 by Wataru Yuasa, Yuasa, Wataru
Mathematics · #20F38 #57M99 #Advanced Algebra and Geometry #FOS: Mathematics #Finite Group Theory Research #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Group Theory (math.GR) #Quantum Algebra (math.QA)
paper · pdf · doi:10.48550/arxiv.1801.06026
openalex publication_date 2018/01/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This paper contains two topics, the index of a power subgroup in the mapping class group M(0,2n) of a 2n-punctured sphere and in the hyperelliptic mapping class group Δ(g,0) of an oriented closed surface of genus g. The main tool is a projective representation of M(0,2n) obtained through the Kauffman bracket skein module. For M(0,2n), we prove that the normal closure of the fifth power of a half-twist has infinite index. This is the remaining case of a Masbaum's work. For Δ(g,0), we consider the normal closure of m-th powers of Dehn twists along all symmetric simple closed curves. We show the subgroup has infinite index if m≥ 5 and m≠ 6 for any g≥ 2.