Orientation-reversing free actions on handlebodies

Details Orientation-reversing free actions on handlebodies Orientation-reversing free actions on handlebodies

2004-11-28

arxiv.org/abs/math/0411624v1

Mathematics

Geometric Topology

Scientific paper

We examine free orientation-reversing group actions on orientable handlebodies, and free actions on nonorientable handlebodies. A classification theorem is obtained, giving the equivalence classes and weak equivalence classes of free actions in terms of algebraic invariants that involve Nielsen equivalence. This is applied to describe the sets of free actions in various cases, including a complete classification for many (and conjecturally all) cases above the minimum genus. For abelian groups, the free actions are classified for all genera.

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