526 citations · 1.1k across the 23 of their papers we have counts for
20 papers · 1 filter
A unified Casson-Lin invariant for the real forms of SL(2)
Nathan M. Dunfield, Jacob Rasmussen
We introduce a unified framework for counting representations of knot groups into and . For a knot in the 3-sphere, Lin and others showed that a Cass…
Heegaard Floer homology for manifolds with torus boundary: properties and examples
Jonathan Hanselman, Jacob Rasmussen, Liam Watson
This is a companion paper to earlier work of the authors, which interprets the Heegaard Floer homology for a manifold with torus boundary in terms of immersed curves in a punctured…
Flag Hilbert schemes, colored projectors and Khovanov-Rozansky homology
Eugene Gorsky, Andrei Neguţ, Jacob Rasmussen
We construct a categorification of the maximal commutative subalgebra of the type Hecke algebra. Specifically, we propose a monoidal functor from the (symmetric) monoidal categ…
Bordered Floer homology for manifolds with torus boundary via immersed curves
Jonathan Hanselman, Jacob Rasmussen, Liam Watson
This paper gives a geometric interpretation of bordered Heegaard Floer homology for manifolds with torus boundary. If is such a manifold, we show that the type D structure $\wi…
L-spaces, taut foliations, and graph manifolds
Jonathan Hanselman, Jacob Rasmussen, Sarah Dean Rasmussen +1
If is a closed orientable graph manifold, we show that admits a coorientable taut foliation if and only if is not an L-space. Combined with previous work of Boyer and C…
Floer Simple Manifolds and L-Space Intervals
Jacob Rasmussen, Sarah Dean Rasmussen
An oriented three-manifold with torus boundary admits either no L-space Dehn filling, a unique L-space filling, or an interval of L-space fillings. In the latter case, which we cal…
On stable Khovanov homology of torus knots
Eugene Gorsky, Alexei Oblomkov, Jacob Rasmussen
We conjecture that the stable Khovanov homology of torus knots can be described as the Koszul homology of an explicit non-regular sequence of quadratic polynomials. The correspondi…
Sutured Floer homology and hypergraphs
András Juhász, Tamás Kálmán, Jacob Rasmussen
By applying Seifert's algorithm to a special alternating diagram of a link L, one obtains a Seifert surface F of L. We show that the support of the sutured Floer homology of the su…
Perfect Morse functions and exotic S^2 x S^2's
Jacob Rasmussen
The main theorem of the paper shows that a smooth manifold which is homeomorphic to S^2xS^2 and has nonvanishing Ozsvath-Szabo invariant does not admit a perfect Morse function. I…
The decategorification of sutured Floer homology
Stefan Friedl, András Juhász, Jacob Rasmussen
We define a torsion invariant T for every balanced sutured manifold (M,g), and show that it agrees with the Euler characteristic of sutured Floer homology SFH. The invariant T is e…
Lens space surgeries and L-space homology spheres
Jacob Rasmussen
We describe necessary and sufficient conditions for a knot in an L-space to have an L-space homology sphere surgery. We use these conditions to reformulate a conjecture of Berge ab…
Some differentials on Khovanov-Rozansky homology
Jacob Rasmussen
We study the relationship between the HOMFLY and sl(N) knot homologies introduced by Khovanov and Rozansky. For each N>0, we show there is a spectral sequence which starts at the H…
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.
The Superpolynomial for Knot Homologies
Nathan M. Dunfield, Sergei Gukov, Jacob Rasmussen
We propose a framework for unifying the sl(N) Khovanov-Rozansky homology (for all N) with the knot Floer homology. We argue that this unification should be accomplished by a triply…
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.
Lens space surgeries and a conjecture of Goda and Teragaito
Jacob Rasmussen
Using work of Ozsvath and Szabo, we show that if a nontrivial knot in S^3 admits a lens space surgery with slope p, then p <= 4g+3, where g is the genus of the knot. This is a clos…
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…
Floer homology of surgeries on two-bridge knots
Jacob Rasmussen
We compute the Ozsvath-Szabo Floer homologies HF^{+-} and HF-hat for three-manifolds obtained by integer surgery on a two-bridge knot.