On wall-crossing coordinates in Cerf theory
Roger Casals
TL;DR
This paper connects Bruhat numbers from real Morse theory to cluster variables in braid varieties, illustrating wall-crossing coordinates within Cerf diagrams to enhance understanding of topological changes.
Contribution
It introduces a novel relationship between Morse theory invariants and cluster algebra structures in the context of Cerf theory.
Findings
Established a link between Bruhat numbers and cluster variables.
Provided examples of wall-crossing coordinates in Cerf diagrams.
Enhanced the understanding of topological transitions in Morse theory.
Abstract
We relate Bruhat numbers in real Morse theory to cluster variables in braid varieties. This provides instances of wall-crossing coordinates in the study of Cerf diagrams.
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Taxonomy
TopicsAdvanced Combinatorial Mathematics · Algebraic structures and combinatorial models · Geometric and Algebraic Topology