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- Title
On independence of iterated Whitehead doubles in the knot concordance group.
- Authors
Park, Kyungbae
- Abstract
Let be the positively clasped untwisted Whitehead double of a knot , and be the torus knot. We show that and are linearly independent in the smooth knot concordance group for each . Further, and generate a summand in the subgroup of generated by topologically slice knots. We use the concordance invariant of Manolescu and Owens, using Heegaard Floer correction term. Interestingly, these results are not easily shown using other concordance invariants such as the -invariant of knot Floer theory and the -invariant of Khovanov homology. We also determine the infinity version of the knot Floer complex of for any generalizing a result for of Hedden, Kim and Livingston.
- Subjects
TORUS knots; CONCORDANCES (Topology); INVARIANTS (Mathematics); HOMOLOGY theory; GROUP theory; INDEPENDENCE (Mathematics)
- Publication
Journal of Knot Theory & Its Ramifications, 2018, Vol 27, Issue 1, p-1
- ISSN
0218-2165
- Publication type
Article
- DOI
10.1142/S0218216518500037