[图书][B] Encyclopedia of knot theory
" Knot theory is a fascinating mathematical subject, with multiple links to theoretical physics.
This enyclopedia is filled with valuable information on a rich and fascinating subject."–Ed …
This enyclopedia is filled with valuable information on a rich and fascinating subject."–Ed …
Khovanov homology for links in# r (S2× S1)
M Willis - Michigan Mathematical Journal, 2021 - projecteuclid.org
We revisit Rozansky's construction of Khovanov homology for links in S2× S1, extending it to
define the Khovanov homology Kh (L) for links L in Mr=# r (S2× S1) for any r. The graded …
define the Khovanov homology Kh (L) for links L in Mr=# r (S2× S1) for any r. The graded …
Field theories, stable homotopy theory and Khovanov homology
P Hu, D Kriz, I Kriz - arXiv preprint arXiv:1203.4773, 2012 - arxiv.org
In this paper, we discuss two topics: first, we show how to convert 1+ 1-topological quantum
field theories valued in symmetric bimonoidal categories into stable homotopical data, using …
field theories valued in symmetric bimonoidal categories into stable homotopical data, using …
Localization in Khovanov homology
M Stoffregen, M Zhang - arXiv preprint arXiv:1810.04769, 2018 - arxiv.org
We construct equivariant Khovanov spectra for periodic links, using the Burnside functor
construction introduced by Lawson, Lipshitz, and Sarkar. By identifying the fixed-point sets …
construction introduced by Lawson, Lipshitz, and Sarkar. By identifying the fixed-point sets …
[HTML][HTML] An odd Khovanov homotopy type
S Sarkar, C Scaduto, M Stoffregen - Advances in Mathematics, 2020 - Elsevier
For each link L⊂ S 3 and every quantum grading j, we construct a stable homotopy type X oj
(L) whose cohomology recovers Ozsváth-Rasmussen-Szabó's odd Khovanov homology, H˜ …
(L) whose cohomology recovers Ozsváth-Rasmussen-Szabó's odd Khovanov homology, H˜ …
Khovanov homology of strongly invertible knots and their quotients
R Lipshitz, S Sarkar - arXiv preprint arXiv:2203.13895, 2022 - arxiv.org
We construct a spectral sequence relating the Khovanov homology of a strongly invertible
knot to the annular Khovanov homologies of the two natural quotient knots. Using this …
knot to the annular Khovanov homologies of the two natural quotient knots. Using this …
Stable homotopy refinement of quantum annular homology
R Akhmechet, V Krushkal, M Willis - Compositio Mathematica, 2021 - cambridge.org
We construct a stable homotopy refinement of quantum annular homology, a link homology
theory introduced by Beliakova, Putyra and Wehrli. For each. The construction relies on an …
theory introduced by Beliakova, Putyra and Wehrli. For each. The construction relies on an …
gl (2) foams and the Khovanov homotopy type
V Krushkal, P Wedrich - arXiv preprint arXiv:2101.05785, 2021 - arxiv.org
The Blanchet link homology theory is an oriented model of Khovanov homology, functorial
over the integers with respect to link cobordisms. We formulate a stable homotopy …
over the integers with respect to link cobordisms. We formulate a stable homotopy …
Khovanov spectra for tangles
Quantum topology began in the 1980s with the Jones polynomial [29] and Witten's
reinterpretation of it via Yang–Mills theory [59]. Witten's work was at a physical level of rigor …
reinterpretation of it via Yang–Mills theory [59]. Witten's work was at a physical level of rigor …
Higher Steenrod squares for Khovanov homology
FC Morán - Advances in Mathematics, 2020 - Elsevier
We describe stable cup-i products on the cochain complex with F 2 coefficients of any
augmented semi-simplicial object in the Burnside category. An example of such an object is …
augmented semi-simplicial object in the Burnside category. An example of such an object is …