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Fixed point free involutions on Riemann surfaces

Hugo Parlier
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Abstract

Involutions without fixed points on hyperbolic closed Riemann surface are discussed. For an orientable surface $X$ of even genus with an arbitrary Riemannian metric $d$ admitting an involution $τ$, it is known that $\min_{p\in X}d(p,τ(p))$ is bounded by a constant which depends on the genus of $X$. The equivalent result is proved to be false in odd genus, and the optimal constant for hyperbolic Riemann surfaces is calculated in genus 2.

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Hugo Parlier. 2005-07-09. Fixed point free involutions on Riemann surfaces. https://arxiv.org/abs/math/0504109

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