New quantum obstructions to sliceness

@article{Lewark2016NewQO,
  title={New quantum obstructions to sliceness},
  author={Lukas Lewark and Andrew Lobb},
  journal={Proceedings of The London Mathematical Society},
  year={2016},
  volume={112},
  pages={81-114}
}
  • Lukas Lewark, Andrew Lobb
  • Published 2016
  • Mathematics
  • Proceedings of The London Mathematical Society
  • It is well known that generic perturbations of the complex Frobenius algebra used to define Khovanov cohomology each give rise to Rasmussen's concordance invariant ss. This gives a concordance homomorphism to the integers and a strong lower bound on the smooth slice genus of a knot. Similar behavior has been observed in sl(n)sl(n) Khovanov–Rozansky cohomology, where a perturbation gives rise to the concordance homomorphisms snsn for each n≥2n≥2, and where we have s2=ss2=s. We demonstrate… CONTINUE READING

    Figures and Tables from this paper.

    Exponential growth of colored HOMFLY-PT homology
    • 19
    • Highly Influenced
    • PDF
    A family of link concordance invariants from perturbed sl(n) homology
    • 3
    • PDF
    Sequencing BPS spectra
    • 42
    • PDF
    A closed formula for the evaluation of $\mathfrak{sl}_N$-foams
    • 11
    • PDF
    Transverse link invariants from the deformations of Khovanov $\mathfrak{sl}_{3}$-homology
    A Bennequin-type inequality and combinatorial bounds.
    • 2
    • PDF
    On webs in quantum type $C$.
    • 1
    • PDF

    References

    Publications referenced by this paper.
    SHOWING 1-10 OF 33 REFERENCES
    On the Quantum Filtration of the Khovanov-rozansky Cohomology
    • 30
    • Highly Influential
    Khovanov homology and the slice genus
    • 437
    • PDF
    Matrix factorizations and link homology II
    • 263
    • PDF
    On Khovanov’s categorification of the Jones polynomial
    • 401
    • PDF
    A note on Gornik's perturbation of Khovanov-Rozansky homology.
    • 15
    • PDF
    A slice genus lower bound from sl(n) Khovanov-Rozansky homology
    • 33
    • PDF
    Concordance homomorphisms from knot Floer homology
    • 106
    • PDF
    Generic deformations of the colored sl(N)-homology for links
    • 14
    • Highly Influential
    • PDF
    Matrix factorizations and link homology
    • 447
    • Highly Influential
    • PDF
    Equivariant sl(n)-link homology
    • 20
    • PDF