Sucharit Sarkar

Moving basepoints and the induced automorphisms of link Floer homology

Given an l-component pointed oriented link (L,p) in an oriented three-manifold Y, one can construct its link Floer chain complex CFL(Y,L,p) over the polynomial ring F_2[U_1,...,U_l]. Moving the basepoint p_i in the link component L_i once around induces an automorphism of CFL(Y,L,p). In this paper, we study an automorphism (a possibly different one) of CFL(Y,L,p) defined explicitly in terms of holomorphic disks; for links in S^3, we show that these two automorphisms are the same.

A Steenrod square on Khovanov homology

In a previous paper, we defined a space-level version X(L) of Khovanov homology. This induces an action of the Steenrod algebra on Khovanov homology. In this paper, we describe the first interesting operation, Sq^2:Kh^{i,j}(L) -> Kh^{i+2,j}(L). We compute this operation for all links up to 11 crossings; this, in turn, determines the stable homotopy type of X(L) for all such links.

On transverse invariants from Khovanov homology

O. Plamenevskaya associated to each transverse knot K an element of the Khovanov homology of K. In this paper, we give two refinements of Plamenevskayas invariant, one valued in Bar-Natans deformation of the Khovanov complex and another as a cohomotopy element of the Khovanov spectrum. We show that the first of these refinements is invariant under negative flypes and SZ moves; this implies that Plamenevskayas class is also invariant under these moves. We go on to show that for small-crossing transverse knots K, both refinements are determined by the classical invariants of K.

Khovanov homology and knot Floer homology for pointed links

A well-known conjecture states that for any

A refinement of Rasmussen’s S-invariant

l

A note on sign conventions in link Floer homology

-component link

Robust estimation in the errors variables model via weighted likelihood estimating equations

L

A perturbation of the geometric spectral sequence in Khovanov homology

in

Commutators and squares in free groups

S^3

A combinatorial description of knot Floer homology

, the rank of the knot Floer homology of