Instanton Floer homology for two-component links
Eric Harper, Nikolai Saveliev
TL;DR
This paper introduces a new instanton Floer homology for two-component links in integral homology spheres, linking it to existing theories and revealing non-vanishing properties for non-split links.
Contribution
It defines a novel Floer homology for two-component links and relates it to Kronheimer-Mrowka's knot Floer homology, providing new insights into link invariants.
Findings
Euler characteristic equals linking number
Floer homology relates to knot Floer homology
Non-vanishing for non-split links in S^3
Abstract
For any link of two components in an integral homology sphere, we define an instanton Floer homology whose Euler characteristic is the linking number between the components of the link. We relate this Floer homology to the Kronheimer-Mrowka instanton Floer homology of knots. We also show that, for two-component links in the 3-sphere, the Floer homology does not vanish unless the link is split.
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Taxonomy
TopicsGeometric and Algebraic Topology · Homotopy and Cohomology in Algebraic Topology · Botulinum Toxin and Related Neurological Disorders