32 citations · 73 across the 12 of their papers we have counts for
14 papers · 1 filter
The decategorification of bordered Khovanov homology
Lawrence Roberts
In two previous papers, the author showed how to decompose the Khovanov homology of a link into the algebraic pairing of a type D structure and a type A structure (as…
Planar algebras and the decategorification of bordered Khovanov homology
Lawrence Roberts
We give a simple, combinatorial construction of a unital, spherical, non-degenerate -planar algebra over the ring . This planar algebra is simil…
On non-isotopic spanning surfaces for a class of arborescent knots
Lawrence Roberts
We use the methods of Hedden, Juhasz, and Sarkar to exhibit a set of arborescent knots that bound large numbers of non-isotopic minimal genus spanning surfaces. In particular, we d…
A type A structure in Khovanov Homology
Lawrence P. Roberts
Inspired by bordered Floer homology, we describe a type A structure on a Khovanov homology for a tangle, which complements the type D structure in a previous paper. The type A stru…
A type D structure in Khovanov homology
Lawrence P. Roberts
We describe the first part of a gluing theory for the bigraded Khovanov homology with integer coefficients. This part associates a type D structure to a tangle properly embedded in…
Twisted skein homology
Nguyen D. Duong, Lawrence P. Roberts
We apply the techniques of totally twisted Khovanov homology to the constructions by M. Asaeda, J. Przytycki, and A. Sikora of Khovanov type homologies for links and tangles in I-b…
Totally Twisted Khovanov Homology
Lawrence Roberts
We define a variation of Khovanov homology with an explicit description in terms of the spanning trees of a link projection. We prove that this new theory is a link invariant and d…
Extending Van Cott's bounds for the -invariant of satellite knots
Lawrence P. Roberts
We generalize C. Van Cott's results on the and -invariants of cabled knots to apply to general satellite knots. This paper uses no Heegaard-Floer homology, relying on more g…
Some bounds for the knot Floer -invariant of satellite knots
Lawrence P. Roberts
We use four dimensional techniques to derive general bounds on the invariant of a satellite knot in .
Notes on the Heegaard-Floer Link Surgery Spectral Sequence
Lawrence Roberts
This largely technical paper is divided into two parts: part I: An account of P. Ozsvath and Z. Szabo's construction of the link surgery spectral sequence. There are no new results…
On knot Floer homology for some fibered knots
Lawrence P. Roberts
A companion paper to "On knot Floer homology in branched double covers" applied to braided branched loci. We reprove the main result of that paper concerning alternating branched l…
On knot Floer homology in double branched covers
Lawrence P. Roberts
Let L be a link in an thickened annulus. We specify the embedding of this annulus in the three sphere, and consider its complement thought of as the axis to L. In the right circums…
Rational blow-downs in Heegaard-Floer homology
Lawrence Roberts
The paper describes how known results in Heegaard-Floer homology apply to all known examples of rational blow-downs, and provides several new four dimensional pieces which could be…
Heegaard-Floer homology and string links
Lawrence Roberts
We extend knot Floer homology to string links in D^{2} \times I and to d-based links in arbitrary three manifolds, without any hypothesis on the null-homology of the components. As…