Knot Floer homology of Whitehead doubles
Hedden, Matthew
Original · EN
In this paper we study the knot Floer homology invariants of the twisted and untwisted Whitehead doubles of an arbitrary knot K. We present a formula for the filtered chain homotopy type of HFK(D(+,K,t)) in terms of the invariants for K, where D(+,K,t) denotes the t-twisted positive-clasped Whitehead double of K. In particular, the formula can be used iteratively and can be used to compute the Floer homology of manifolds obtained by surgery on Whitehead doubles. An immediate corollary is that tau(D(+,K,t))=1 if t< 2tau(K) and zero otherwise, where tau is the Ozsváth-Szabó concordance invariant. It follows that the iterated untwisted Whitehead doubles of a knot satisfying tau(K)>0 are not smoothly slice.
English translation
This paper has no Arabic translation yet. Be the first: it takes a few seconds, and the result is stored for every future reader.