Canonical Symplectic Representations for Prime Order Conjugacy Classes of the Mapping-class Group

Jane Gilman

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Canonical Symplectic Representations for Prime Order Conjugacy Classes of the Mapping-class Group

Jane Gilman

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Abstract

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.

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Jane Gilman. 2007-06-17. Canonical Symplectic Representations for Prime Order Conjugacy Classes of the Mapping-class Group. https://arxiv.org/abs/math/0701330

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