Stable functions and common stabilizations of Heegaard splittings

Details Stable functions and common stabilizations of Heegaard splittings Stable functions and common stabilizations of Heegaard splittings

2007-05-25

arxiv.org/abs/0705.3712v1

Mathematics

Geometric Topology

24 pages, 10 figures

Scientific paper

We present a new proof of Reidemeister and Singer's Theorem that any two
Heegaard splittings of the same 3-manifold have a common stabilization. The
proof leads to an upper bound on the minimal genus of a common stabilization in
terms of the number of negative slope inflection points and type-two cusps in a
Rubinstein-Scharlemann graphic for the two splittings.

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