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Locally unknotted spines of Heegaard splittings. (English) Zbl 1120.57007
The main result of this paper is the following: If \((\Sigma, H_1, H_2)\) is a strongly irreducible Heegaard splitting for a manifold \(M\) then every spine of \(\Sigma\) is locally unknotted. Thus the spines of the handlebodies of a strongly irreducible Heegaard splitting will intersect a closed ball in a graph which is isotopic into the boundary of the ball.

57M27 Invariants of knots and \(3\)-manifolds (MSC2010)
57Q10 Simple homotopy type, Whitehead torsion, Reidemeister-Franz torsion, etc.
Full Text: DOI EuDML arXiv
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