Knot homology groups from instantons
P. B. Kronheimer, T. S. Mrowka
TL;DR
This paper introduces a new Floer homology theory for knots in 3-manifolds derived from instantons with singularities, expanding the toolkit for knot invariants using gauge theory.
Contribution
It defines a novel Floer homology framework for knots based on instantons with codimension-2 singularities in partial flag manifolds of SU(N).
Findings
Establishment of a Floer homology theory for knots.
Application to partial flag manifolds of SU(N).
Potential for new knot invariants.
Abstract
For each partial flag manifold of SU(N), we define a Floer homology theory for knots in 3-manifolds, using instantons with codimension-2 singularities.
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