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  • DG structures on odd categorified quantum $sl(2)$
    Quantum Topol. (IF 1.083) Pub Date : 2020-06-22
    Ilknur Egilmez; Aaron D. Lauda

    We equip Ellis and Brundan’s version of the odd categorified quantum group for $sl(2)$ with a differential giving it the structure of a graded dg-2-supercategory. The presence of the super grading gives rise to two possible decategorifications of the associated dg-2-category. One version gives rise to a categorification of quantum $sl(2)$ at a fourth root of unity, while the other version produces

    更新日期:2020-07-20
  • Contact (+1)-surgeries along Legendrian two-component links
    Quantum Topol. (IF 1.083) Pub Date : 2020-06-21
    Fan Ding; Youlin Li; Zhongtao Wu

    In this paper, we study contact surgeries along Legendrian links in the standard contact 3-sphere. On one hand, we use algebraic methods to prove the vanishing of the contact Ozsváth–Szabó invariant for contact (+1)-surgery along certain Legendrian two-component links. The main tool is a link surgery formula for Heegaard Floer homology developed by Manolescu and Ozsváth. On the other hand, we use contact-geometric

    更新日期:2020-07-20
  • Surgery on links of linking number zero and the Heegaard Floer $d$-invariant
    Quantum Topol. (IF 1.083) Pub Date : 2020-06-21
    Eugene Gorsky; Beibei Liu; Allison H. Moore

    We study Heegaard Floer homology and various related invariants (such as the $h$-function) for two-component L-space links with linking number zero. For such links, we explicitly describe the relationship between the $h$-function, the Sato–Levine invariant and the Casson invariant. We give a formula for the Heegaard Floer $d$-invariants of integral surgeries on two-component L-space links of linking

    更新日期:2020-07-20
  • Torelli group, Johnson kernel, and invariants of homology spheres
    Quantum Topol. (IF 1.083) Pub Date : 2020-06-24
    Shigeyuki Morita; Takuya Sakasai; Masaaki Suzuki

    In the late 1980s, it was shown that the Casson invariant appears in the difference between the two filtrations of the Torelli group: the lower central series and the Johnson filtration, and its core part was identified with the secondary characteristic class $d_1$ associated with the fact that the first $\mathrm{MMM}$ class vanishes on the Torelli group (however it turned out that Johnson proved the

    更新日期:2020-07-20
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