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of 24
pro vyhledávání: '"Akhmechet, Rostislav"'
We introduce an invariant of negative definite plumbed knot complements unifying knot lattice homology, due to Ozsv\'ath, Stipsicz, and Szab\'o, and the BPS $q$-series of Gukov and Manolescu. This invariant is a natural extension of weighted graded r
Externí odkaz:
http://arxiv.org/abs/2403.14461
Autor:
Akhmechet, Rostislav
We introduce equivariant $\mathfrak{gl}_N$ homology for links in the thickened annulus via foam evaluation.
Comment: 23 pages, many figures
Comment: 23 pages, many figures
Externí odkaz:
http://arxiv.org/abs/2305.08944
Autor:
Akhmechet, Rostislav, Zhang, Melissa
We study Khovanov homology over the Frobenius algebra $\mathbb{F}[U,V,X]/((X-U)(X-V))$, or $U(1) \times U(1)$-equivariant Khovanov homology, and extract two families of concordance invariants using the algebraic $U$-power and $V$-power filtrations on
Externí odkaz:
http://arxiv.org/abs/2210.10731
Publikováno v:
J. Reine Angew. Math. 796 (2023), 269-299
An invariant is introduced for negative definite plumbed $3$-manifolds equipped with a spin$^c$-structure. It unifies and extends two theories with rather different origins and structures. One theory is lattice cohomology, motivated by the study of n
Externí odkaz:
http://arxiv.org/abs/2109.14139
Publikováno v:
Algebr. Geom. Topol. 23 (2023) 3129-3204
We describe equivariant SL(2) and SL(3) homology for links in the solid torus via foam evaluation. The solid torus is replaced by 3-space with a distinguished line in it. Generators of state spaces for annular webs are represented by foams with bound
Externí odkaz:
http://arxiv.org/abs/2105.00921
Publikováno v:
Adv. Math. 408 (2022), part A, Paper No. 108581
Given a link in the thickened annulus, its annular Khovanov homology carries an action of the Lie algebra $\mathfrak{sl}_2$, which is natural with respect to annular link cobordisms. We consider the problem of lifting this action to the stable homoto
Externí odkaz:
http://arxiv.org/abs/2011.11234
Autor:
Akhmechet, Rostislav
We construct an equivariant version of annular Khovanov homology via the Frobenius algebra associated with $U(1) \times U(1)$-equivariant cohomology of $\mathbb{CP}^1$. Motivated by the relationship between the Temperley-Lieb algebra and annular Khov
Externí odkaz:
http://arxiv.org/abs/2008.00577
Publikováno v:
Compositio Math. 157 (2021) 710-769
We construct a stable homotopy refinement of quantum annular homology, a link homology theory introduced by Beliakova, Putyra and Wehrli. For each $r\geq 2$ we associate to an annular link $L$ a naive $\mathbb{Z}/r\mathbb{Z}$-equivariant spectrum who
Externí odkaz:
http://arxiv.org/abs/2001.00077
Publikováno v:
In Advances in Mathematics 29 October 2022 408 Part A
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