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- Title
The space of Heegaard splittings.
- Authors
Johnson, Jesse; McCullough, Darryl
- Abstract
For a Heegaard surface Σ in a closed orientable 3-manifold M, we denote by ℋ( M, Σ) = Diff( M)/Diff( M, Σ) the space of Heegaard surfaces equivalent to the Heegaard splitting ( M, Σ). Its path components are the isotopy classes of Heegaard splittings equivalent to ( M, Σ). We describe H( M, Σ) in terms of Diff( M) and the Goeritz group of ( M, Σ). In particular, for hyperbolic M each path component is a classifying space for the Goeritz group, and when the (Hempel) distance of ( M, Σ) is greater than 3, each path component of ℋ( M, Σ) is contractible. For splittings of genus 0 or 1, we determine the complete homotopy type (modulo the Smale Conjecture for M in the cases when it is not known).
- Subjects
MINIMAL surfaces; MAXIMA &; minima; GAUSS maps; PLATEAU'S problem; CALCULUS of variations
- Publication
Journal für die Reine und Angewandte Mathematik, 2013, Vol 2013, Issue 679, p155
- ISSN
0075-4102
- Publication type
Article
- DOI
10.1515/crelle.2012.016