2007/01/11 by Jane Gilman, Gilman, Jane
Mathematics · #14H15 #14H55 #20H10 #30F10 #30F40 #32G15 #57M60 #Advanced Topics in Algebra #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Group Theory (math.GR) #Homotopy and Cohomology in Algebraic Topology #math.GR #math.GT #msc:14H15 #msc:14H55 #msc:20H10 #msc:30F10 #msc:30F40 #msc:32G15 #msc:57M60
paper · pdf · doi:10.48550/arxiv.math/0701330
24 pages; change in title; typos corrected; some theorems revised; computational complexity added; final version of paper to appear in Journal of Algebra
openalex publication_date 2007/01/11 · arxiv created 2007/06/17 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper we find a unique normal form for the symplectic matrix representation of the conjugacy class of a prime order element of the mapping-class group. We find a set of generators for the fundamental group of a surface with a conformal automorphism of prime order which reflects the action the automorphism in an optimal way. This is called an \sl adapted homotopy basis and there is a corresponding \sl adapted presentation. We also give a necessary and sufficient condition for a prime order symplectic matrix to be the image of a prime order element in the mapping-class group.