A refinement of Rasmussen's s-invariant
By Robert Lipshitz, Sucharit Sarkar. 2012
76 citations recorded by the source corpus.
In a previous paper we constructed a spectrum-level refinement of Khovanov homology. This refinement induces stable cohomology operations on Khovanov homology. In this paper we show that these cohomology operations commute with cobordism maps on Khovanov homology. As a consequence we obtain a refinement of Rasmussen's slice genus bound s for each stable cohomology operation. We show that in the case of the Steenrod square Sq^2 our refinement is strictly stronger than s.
Subfields: Discrete Mathematics and Combinatorics, Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/55fa7ce6d7d0b110cc35919ad6fb36c96fa54b80
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Discrete Mathematics and Combinatorics
- A. Stipsicz
- Peter S. Ozsv'ath
- Zolt'an Szab'o
- Ciprian Manolescu
- Jacob Rasmussen
- P. Lisca
- John A. Baldwin
- M. Hedden
In Geometry and Topology
- A. Stipsicz
- Peter S. Ozsv'ath
- Zolt'an Szab'o
- Ciprian Manolescu
- P. Lisca
- Jacob Rasmussen
- John A. Baldwin
- M. Hedden
In Mathematical Physics
- A. Stipsicz
- Peter S. Ozsv'ath
- Zolt'an Szab'o
- Ciprian Manolescu
- Jacob Rasmussen
- M. Hedden
- John A. Baldwin
- Ian Zemke
Citations in the corpus
- Grid Homology for Knots and Links (2015, background): “) For more questions along these lines for Khovanov homology, see Section 6 of [123].”
- On the geography and botany of knot Floer homology (2014, unknown): “5 (Rasmussen [83], Lipshitz-Sarkar [50]) For any knot K , |s̃(K )| ≤ g4(K ).”