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pro vyhledávání: '"Sarkar, Sucharit"'
These notes provide an introduction to the stable homotopy types in Khovanov theory (due to Lipshitz-Sarkar) and in knot Floer theory (due to Manolescu-Sarkar). They were written following a lecture series given by Sucharit Sarkar at the Renyi Instit
Externí odkaz:
http://arxiv.org/abs/2401.06218
Autor:
Lipshitz, Robert, Sarkar, Sucharit
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 spectral sequence, we re-prove that Khovanov homology distinguishes certain
Externí odkaz:
http://arxiv.org/abs/2203.13895
The aim of this paper is to study the behavior of knot Floer homology under Murasugi sum. We establish a graded version of Ni's isomorphism between the extremal knot Floer homology of Murasugi sum of two links and the tensor product of the extremal k
Externí odkaz:
http://arxiv.org/abs/2202.09041
Autor:
Lipshitz, Robert, Sarkar, Sucharit
We construct a mixed invariant of non-orientable surfaces from the Lee and Bar-Natan deformations of Khovanov homology and use it to distinguish pairs of surfaces bounded by the same knot, including some exotic examples.
Comment: 43 pages, 7 fig
Comment: 43 pages, 7 fig
Externí odkaz:
http://arxiv.org/abs/2109.09018
Autor:
Manolescu, Ciprian, Sarkar, Sucharit
Given a grid diagram for a knot or link K in $S^3$, we construct a spectrum whose homology is the knot Floer homology of K. We conjecture that the homotopy type of the spectrum is an invariant of K. Our construction does not use holomorphic geometry,
Externí odkaz:
http://arxiv.org/abs/2108.13566
We prove that the Khovanov spectra associated to links and tangles are functorial up to homotopy and sign.
Comment: 45 pages, 6 figures. V2: add discussion of neck cutting and ribbon concordances. V3: minor revisions. Accepted for publication in
Comment: 45 pages, 6 figures. V2: add discussion of neck cutting and ribbon concordances. V3: minor revisions. Accepted for publication in
Externí odkaz:
http://arxiv.org/abs/2104.12907
We extend the definition of Khovanov-Lee homology to links in connected sums of $S^1 \times S^2$'s, and construct a Rasmussen-type invariant for null-homologous links in these manifolds. For certain links in $S^1 \times S^2$, we compute the invariant
Externí odkaz:
http://arxiv.org/abs/1910.08195
Autor:
Lipshitz, Robert, Sarkar, Sucharit
Extending ideas of Hedden-Ni, we show that the module structure on Khovanov homology detects split links. We also prove an analogue for untwisted Heegaard Floer homology of the branched double cover. Technical results proved along the way include two
Externí odkaz:
http://arxiv.org/abs/1910.04246
We note that our stable homotopy refinements of Khovanov's arc algebras and tangle invariants induce refinements of Chen-Khovanov and Stroppel's platform algebras and tangle invariants, and discuss the topological Hochschild homology of these refinem
Externí odkaz:
http://arxiv.org/abs/1909.12994
Autor:
Sarkar, Sucharit
Publikováno v:
Algebr. Geom. Topol. 20 (2020) 1041-1058
We study a notion of distance between knots, defined in terms of the number of saddles in ribbon concordances connecting the knots. We construct a lower bound on this distance using the X-action on Lee's perturbation of Khovanov homology.
Commen
Commen
Externí odkaz:
http://arxiv.org/abs/1903.11095