A proof of the Gordon Conjecture
Ruifeng Qiu, Martin Scharlemann
TL;DR
This paper provides a combinatorial proof of the Gordon Conjecture, establishing a key relationship between the stabilization of Heegaard splittings and their summands.
Contribution
It offers the first combinatorial proof of the Gordon Conjecture, advancing understanding of Heegaard splitting stabilization.
Findings
Sum of two Heegaard splittings is stabilized iff one summand is stabilized
Provides a combinatorial proof for the Gordon Conjecture
Clarifies the relationship between stabilization and summands
Abstract
A combinatorial proof of the Gordon Conjecture: The sum of two Heegaard splittings is stabilized if and only if one of the two summands is stabilized.
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Taxonomy
TopicsHistory and Theory of Mathematics · Advanced Topology and Set Theory · Mathematics and Applications