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GAIA Seminar - Kyungbae Park (Michigan State University)

posted May 29, 2013, 12:26 AM by Jihye Jung   [ updated Jun 3, 2013, 11:32 PM ]
- Title : On Independence of Iterated Whitehead Doubles in the Knot Concordance Group
- Speaker : Kyungbae Park (Michigan State University)
- Date : 11 a.m.- 12(Noon),Friday, 31 May 2013
- Place : The GAIA (Math Science building room 106)
- Abstract

  Let D(K) be the positively-clasped untwisted Whitehead double of a knot K, and T(p, q) be the (p, q) torus knot. We show that D(T(2, 2m+1)) and D(D(T(2, 2m+1))) differ in the smooth concordance group of knots for each m>1. In fact, they generate a Z2 summand in the subgroup generated by topologically slice knots. We use the concordance invariant δ by Manolescu and Owens. More generally, we show that the same result holds for a knot K with |δ(D(K))|>8 and give a formula to compute δ(D(K)) for some classes of knots. Interestingly, these results are not easily be shown using other concordance invariants such as the knot signature and τ-invariants of the knot Floer theory. We also determine the knot Floer complex of D(T(2, 2m+1)) for any m>0 generalizing a result for T(2, 3) of Hedden, Kim and Livingston.



- Contact: Jihye Jung (POSTECH, Tel. 279-8020)



Jihye Jung,
Jun 3, 2013, 11:33 PM