Canonical Symplectic Representations for Prime Order Conjugacy Classes of the Mapping-class Group
Abstract
Description
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.
24 pages; change in title; typos corrected; some theorems revised; computational complexity added; final version of paper to appear in Journal of Algebra
24 pages; change in title; typos corrected; some theorems revised; computational complexity added; final version of paper to appear in Journal of Algebra