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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 fr , from the knot concordance group to R. 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.
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A note on cables and the involutive concordance invariants
Abstract We prove a formula for the involutive concordance invariants of the cabled knots in terms of those of the companion knot and the pattern knot. As a consequence, we show that any iterated cable of a knot with parameters of the form (odd,1) is not smoothly slice as long as either of the involutive concordance invariants of the knot is nonzero. Our formula also gives new bounds for the unknotting number of a cabled knot, which are sometimes stronger than other known bounds coming from knot Floer homology.
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- Award ID(s):
- 2019396
- PAR ID:
- 10577326
- Publisher / Repository:
- Oxford University Press (OUP)
- Date Published:
- Journal Name:
- Bulletin of the London Mathematical Society
- Volume:
- 57
- Issue:
- 5
- ISSN:
- 0024-6093
- Format(s):
- Medium: X Size: p. 1593-1604
- Size(s):
- p. 1593-1604
- Sponsoring Org:
- National Science Foundation
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