Orientation-reversing involutions on handlebodies

Kalliongis, John; McCullough, Darryl

doi:10.1090/S0002-9947-96-01515-2

Orientation-reversing involutions on handlebodies
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by John Kalliongis and Darryl McCullough PDF

Trans. Amer. Math. Soc. 348 (1996), 1739-1755 Request permission

Abstract:

The observation that the quotient orbifold of an orientation- reversing involution on a 3-dimensional handlebody has the structure of a compression body leads to a strong classification theorem, and general structure theorems. The structure theorems decompose the action along invariant discs into actions on handlebodies which preserve the $I$-fibers of some $I$-bundle structure. As applications, various results of R. Nelson are proved without restrictive hypotheses.

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