Sutured Khovanov homology distinguishes braids from other tangles
J. Elisenda Grigsby, Yi Ni
TL;DR
This paper proves that sutured Khovanov homology can uniquely identify when a balanced tangle in a product sutured manifold is isotopic to a braid, providing a new topological invariant for braids.
Contribution
It establishes a characterization of braids via sutured Khovanov homology, demonstrating that rank 1 homology precisely corresponds to braid isotopy classes.
Findings
Rank 1 sutured Khovanov homology characterizes braids.
Non-braid tangles have higher homology rank.
Provides a new invariant for distinguishing braids from other tangles.
Abstract
We show that the sutured Khovanov homology of a balanced tangle in the product sutured manifold D x I has rank 1 if and only if the tangle is isotopic to a braid.
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Taxonomy
TopicsGeometric and Algebraic Topology · Homotopy and Cohomology in Algebraic Topology · Botulinum Toxin and Related Neurological Disorders