526 citations · 600 across the 5 of their papers we have counts for
6 papers
Khovanov-Rozansky homology of two-bridge knots and links
Jacob Rasmussen
We compute the reduced version of Khovanov and Rozansky's sl(N) homology for two-bridge knots and links. The answer is expressed in terms of the HOMFLY polynomial and signature.
Knot polynomials and knot homologies
Jacob Rasmussen
This is an expository paper discussing some parallels between the Khovanov and knot Floer homologies. We describe the formal similarities between the theories and give some example…
Khovanov's invariant for closed surfaces
Jacob Rasmussen
We compute the Khovanov-Jacobsson number of an embedded torus in R^4. The answer is always 2, regardless of the embedding.
Khovanov homology and the slice genus
Jacob A. Rasmussen
We use Lee's work on the Khovanov homology to define a knot invariant s. We show that s(K) is a concordance invariant and that it provides a lower bound for the slice genus of K. A…
Floer homology and knot complements
Jacob Rasmussen
We use the Ozsvath-Szabo theory of Floer homology to define an invariant of knot complements in three-manifolds. This invariant takes the form of a filtered chain complex, which we…
Induced Topology on the Hoop Group
J. Rasmussen, M. Weis
A new topology is proposed on the space of holonomy equivalence classes of loops, induced by the topology of the space in which the loops are embedded. The possible role for th…