A homological action on sutured instanton homology
Hongjian Yang
TL;DR
This paper introduces a new homological action on sutured instanton Floer homology, demonstrating its well-defined nature and applications in detecting link splitting in two-component links.
Contribution
It defines a homological action on sutured instanton Floer homology and proves its invariance and compatibility with topological operations.
Findings
Homological action is well-defined up to scalars.
Action behaves well under connected sums and decompositions.
Detects link splitting in two-component links.
Abstract
We define a homological action on sutured instanton Floer homology. This action is well-defined up to scalars, and behaves well under connected sums and sutured manifold decompositions. As an application, we show that instanton knot homology detects link splitting for two-component links.
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Taxonomy
TopicsGeometric and Algebraic Topology · Botulinum Toxin and Related Neurological Disorders