Concordance groups of links

Abstract

We define a notion of concordance based on Euler characteristic, and show that it gives rise to a concordance group of links in the three-sphere, which has the concordance group of knots as a direct summand with infinitely generated complement. We consider variants of this using oriented and nonoriented surfaces as well as smooth and locally flat embeddings.

21 pages, 6 figures

References in corpus (5)

• Lens spaces, rational balls and the ribbon conjecture
• Sums of lens spaces bounding rational balls
• Scissor equivalence for torus links
• The nonorientable four-genus of knots
• Smooth concordance of links topologically concordant to the Hopf link

Cited by in corpus (11)

• On the Frøyshov invariant and monopole Lefschetz number
• Unlinking information from 4-manifolds
• Embedding 3-manifolds in spin 4-manifolds
• Surgeries on torus knots, rational balls, and cabling
• Ribbon cobordisms between lens spaces
• Black magic session of concordance: Regge mass spectrum from Casson's invariant
• Locally equivalent Floer complexes and unoriented link cobordisms
• On slice alternating 3-braid closures
• Signatures, Heegaard Floer correction terms and quasi-alternating links
• A Note on Pure Braids and Link Concordance
• Generalized Heegaard Floer correction terms