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  • Homological algebra related to surfaces with boundary
    Quantum Topol. (IF 1.083) Pub Date : 2020-12-23
    Kai Cieliebak; Kenji Fukaya; Janko Latschev

    In this article we describe an algebraic framework which can be used in three related but different contexts: string topology, symplectic field theory, and Lagrangian Floer theory of higher genus.

    更新日期:2020-12-24
  • A Hennings type invariant of 3-manifolds from a topological Hopf superalgebra
    Quantum Topol. (IF 1.083) Pub Date : 2020-10-21
    Ngoc Phu Ha

    We prove the unrolled superalgebra $\mathcal{U}_{\xi}^{H}\mathfrak{sl}(2|1)$ has a completion which is a ribbon Hopf superalgebra in a topological sense where $\xi$ is a root of unity of odd order. Using this ribbon Hopf superalgebra we construct its universal invariant of links. We use it to construct an invariant of $3$\nbdash manifolds endowed with a first cohomology class of Hennings type.

    更新日期:2020-12-23
  • Goldman–Turaev formality implies Kashiwara–Vergne
    Quantum Topol. (IF 1.083) Pub Date : 2020-10-21
    Anton Alekseev; Nariya Kawazumi; Yusuke Kuno; Florian Naef

    Let $\Sigma$ be a compact connected oriented 2-dimensional manifold with non-empty boundary. In our previous work, we have shown that every solution of the higher genus Kashiwara–Vergne equations for an automorphism $F \in \mathrm {aut}(L)$ of a free Lie algebra induces an isomorphism between the Goldman–Turaev Lie bialgebra $\mathfrak{g}(\Sigma)$ and its associated graded gr $\mathfrak{g}(\Sigma)$

    更新日期:2020-12-23
  • The Strong Slope Conjecture for twisted generalized Whitehead doubles
    Quantum Topol. (IF 1.083) Pub Date : 2020-10-11
    Kenneth L. Baker; Kimihiko Motegi; Toshie Takata

    The Slope Conjecture proposed by Garoufalidis asserts that the degree of the colored Jones polynomial determines a boundary slope, and its refinement, the Strong Slope Conjecture proposed by Kalfagianni and Tran asserts that the linear term in the degree determines the topology of an essential surface that satisfies the Slope Conjecture. Under certain hypotheses, we show that twisted, generalized Whitehead

    更新日期:2020-10-12
  • A closed formula for the evaluation of foams
    Quantum Topol. (IF 1.083) Pub Date : 2020-08-22
    Louis-Hadrien Robert; Emmanuel Wagner

    We give a purely combinatorial formula for evaluating closed, decorated foams. Our evaluation gives an integral polynomial and is directly connected to an integral, equivariant version of colored Khovanov–Rozansky link homology categorifying the $\mathfrak {sl}_N$ link polynomial. We also provide connections to the equivariant cohomology rings of partial flag varieties.

    更新日期:2020-10-11
  • Prime decomposition of modular tensor categories of local modules of type D
    Quantum Topol. (IF 1.083) Pub Date : 2020-09-24
    Andrew Schopieray

    Let $\mathcal{C}(\mathfrak{g},k)$ be the unitary modular tensor categories arising from the representation theory of quantum groups at roots of unity for arbitrary simple finite-dimensional complex Lie algebra $\mathfrak{g}$ and positive integer levels $k$. Here we classify nondegenerate fusion subcategories of the modular tensor categories of local modules $\mathcal{C}(\mathfrak{g},k)_R^0$ where $R$

    更新日期:2020-10-11
  • Ore's theorem on subfactor planar algebras
    Quantum Topol. (IF 1.083) Pub Date : 2020-09-24
    Sébastien Palcoux

    This article proves that an irreducible subfactor planar algebra with a distributive biprojection lattice admits a minimal 2-box projection generating the identity biprojection. It is a generalization (conjectured in 2013) of a theorem of Øystein Ore on distributive intervals of finite groups (1938), and a corollary of a natural subfactor extension of a conjecture of Kenneth S. Brown in algebraic combinatorics

    更新日期:2020-10-11
  • 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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