84 research outputs found
Period three actions on the three-sphere
We show that a free period three action on the three-sphere is standard, i.e.
the quotient is homeomorphic to a lens space. We use a minimax argument
involving sweepouts.Comment: Published by Geometry and Topology at
http://www.maths.warwick.ac.uk/gt/GTVol7/paper11.abs.htm
Genus two Heegaard splittings of orientable three-manifolds
It was shown by Bonahon-Otal and Hodgson-Rubinstein that any two genus-one
Heegaard splittings of the same 3-manifold (typically a lens space) are
isotopic. On the other hand, it was shown by Boileau, Collins and Zieschang
that certain Seifert manifolds have distinct genus-two Heegaard splittings. In
an earlier paper, we presented a technique for comparing Heegaard splittings of
the same manifold and, using this technique, derived the uniqueness theorem for
lens space splittings as a simple corollary. Here we use a similar technique to
examine, in general, ways in which two non-isotopic genus-two Heegard
splittings of the same 3-manifold compare, with a particular focus on how the
corresponding hyperelliptic involutions are related.Comment: 65 pages. Published copy, also available at
http://www.maths.warwick.ac.uk/gt/GTMon2/paper24.abs.htm
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