Extending finite group actions from surfaces to handlebodies

  title={Extending finite group actions from surfaces to handlebodies},
  author={Marco Reni and Bruno Zimmermann},
We show that every action of a finite dihedral group on a closed orientable surface F extends to a 3-dimensional handlebody V , with ∂V = F . In the case of a finite abelian group G, we give necessary and sufficient conditions for a G-action on a surface to extend to a compact 3-manifold, or, equivalently in this case, to a 3-dimensional handlebody; in particular all (fixed-point) free actions of finite abelian groups extend to handlebodies. This is no longer true for free actions of arbitrary… 

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