Instantons and some concordance invariants of knots

Abstract

Concordance invariants of knots are derived from the instanton homology groups with local coefficients, as introduced in earlier work of the authors. These concordance invariants include a 1-parameter family of homomorphisms $f_r$, from the knot concordance group to the reals. Prima facie, these concordance invariants have the potential to provide independent bounds on the genus and number of double points for immersed surfaces with boundary a given knot.

This paper, together with a companion paper "Instantons and Bar-Natan homology", supersedes the authors' earlier preprint, "Instantons, Bar-Natan homology and some concordance invariants of knots"

References in corpus (3)

• Khovanov homology and ribbon concordance
• The Bar-Natan homology and unknotting number
• Knot Floer homology and the unknotting number

Cited by in corpus (5)

• Equivariant aspects of singular instanton Floer homology
• Non-orientable link cobordisms and torsion order in Floer homologies
• Instantons, special cycles, and knot concordance
• Cables of the figure-eight knot via real Frøyshov invariants
• Relations in singular instanton homology