The Rasmussen Invariant of a Homogeneous Knot

On Simplification of the Combinatorial Link Floer Homology

We give a new combinatorial construction of the hat version of the link Floer homology over Z/2Z and verify that in many examples, our complex is smaller than Manolescu–Ozsváth–Sarkar one. Introduction Knot Floer homology is a powerful knot invariant constructed by Ozsváth–Szabo [11] and Rasmussen [14]. In its basic form, the knot Floer homology ĤFK(K) of a knot K ∈ S is a finite–dimensional bi...

A Remark on Rasmussen’s Invariant of Knots

We show that Rasmussen’s invariant of knots, which is derived from Lee’s variant of Khovanov homology, is equal to an analogous invariant derived from certain other filtered link homologies.

Convolution and Homogeneous Spaces

A Combinatorial Description of Some Heegaard Floer Homologies

Heegaard Floer homology is a 3-manifold invariant introduced by Peter Ozsváth and Zoltán Szabó [3]. There are four versions, denoted by ĤF ,HF∞,HF+ and HF−, which are graded abelian groups satisfying certain long exact sequences. A knot K in a 3-manifold Y induces a filtration of ĈF (Y ), and the filtration type is a knot invariant. The successive quotients give a knot invariant ĤFK(K,Y ), whic...

‎On the two-wavelet localization operators on homogeneous spaces with relatively invariant measures

In ‎the present ‎paper, ‎we ‎introduce the ‎two-wavelet ‎localization ‎operator ‎for ‎the square ‎integrable ‎representation ‎of a‎ ‎homogeneous space‎ with respect to a relatively invariant measure. ‎We show that it is a bounded linear operator. We investigate ‎some ‎properties ‎of the ‎two-wavelet ‎localization ‎operator ‎and ‎show ‎that ‎it ‎is a‎ ‎compact ‎operator ‎and is ‎contained ‎in‎ a...