Khovanov homology is an unknot-detector

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August undefined, 2024

WebKhovanov homology is an unknot-detector. We prove that a knot is the unknot if and only if its reduced Khovanov cohomology has rank 1. The proof has two steps. We … WebKhovanov homology is an unknot-detector Item Preview remove-circle Share or Embed This Item. Share to Twitter. Share to Facebook. Share to Reddit. Share to Tumblr. Share …

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WebCiteSeerX - Document Details (Isaac Councill, Lee Giles, Pradeep Teregowda): Abstract. We prove that a knot is the unknot if and only if its reduced Khovanov cohomology has rank 1. The proof has two steps. We show first that there is a spectral sequence beginning with the reduced Khovanov cohomology and abutting to a knot homology defined using … WebKronheimer and Mrowka (2010) proved Khovanov homology is an unknot detector using gauge theory. The conjecture is known to be true in many cases. COMPUTATIONS … atasehir kiralik esyali daire

arXiv:1907.12194v4 [math.QA] 28 Jun 2024

WebIn mathematics, Khovanov homology is an oriented link invariant that arises as the cohomology of a cochain complex. It may be regarded as a categorification of the Jones polynomial . It was developed in the late 1990s by Mikhail Khovanov, then at the University of California, Davis, now at Columbia University . Contents 1 Overview 2 Definition Web29 aug. 2024 · , Khovanov homology is an unknot-detector, Publ. Math. Inst. HautesÉtudes Sci. 113 (2011), 97-208. MR2805599 [KM11b] , Knot homology groups from instantons, J. Topol. 4 (2011), no. 4, 835-918.... WebWe prove that a knot is the unknot if and only if its reduced Khovanov cohomology has rank 1. The proof has two steps. We show first that there is a spectral sequence … atascadero baseball

$arXiv:1809.01568v2 [math.GT] 21 Jun 2024$

Khovanov homology is an unknot-detector

WebAbstract We apply the Rasmussen spectral sequence to prove that the ℤ 3 -graded vector space structure of the HOMFLYPT homology over ℤ 2 detects unlinks. Our proof relies on a theorem of Batson and Seed stating that the ℤ 2 -graded vector space structure of the Khovanov homology over ℤ 2 detects unlinks. Keywords: HOMFLYPT homology Web7.Peter B. Kronheimer and Tomasz S. Mrowka, Khovanov homology is an unknot-detector, Publications Math ematiques de l’IHES 113 (2011), no. 1, 97{208. 8.Eun Soo Lee, The support of the Khovanov’s invariants for alternating knots, preprint, arXiv:math/0201105 (2002).

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WebKhovanov homology is an unknot-detector P. B. Kronheimer and T. S. Mrowka Publ. Math. Inst. Hautes Études Sci. Poscript: Instanton Floer homology and the Alexander polynomial P. B. Kronheimer and T. S. Mrowka Algebraic and Geometric Topology: Poscript: Knots, sutures and excision ... WebKhovanov homology and Floer homology theories in diﬀerent settings has been studied a lot. The ﬁrst such result is due to Ozsv´ath and ... as well as the unknot detection result in [KM11]. Khovanov also deﬁned a sequence of invariants Khrn(K) of a knot K ⊂ S3 which categorify the (reduced) n-colored Jones polynomials in [Kho05]. In ...

WebKHOVANOV HOMOLOGY IS AN UNKNOT-DETECTOR by P. B. KRONHEIMER and T. S. MROWKA ABSTRACT We prove that a knot is the unknot if and only if its reduced … WebKhovanov homology is an unknot-detector P. Kronheimer, T. Mrowka Published 24 May 2010 Mathematics Publications mathématiques de l'IHÉS We prove that a knot is the …

WebWe prove that a knot is the unknot if and only if its reduced Khovanov cohomology has rank 1. The proof has two steps. We show first that there is a spectral sequence beginning with the reduced Khovanov cohomology and abutting to a knot homology defined using singular instantons. WebKhovanov homology is an unknot-detector P. B. Kronheimer and T. S. Mrowka Harvard University, Cambridge MA 02138 Massachusetts Institute of Technology, Cambridge MA …

Web5 nov. 2024 · The Jones polynomial is a famous link invariant that can be defined diagrammatically via a skein relation. Khovanov homology is a richer link invariant that categorifies the Jones polynomial. Using spectral sequences, we obtain a skein-type relation satisfied by the Khovanov homology.

Web9 aug. 2008 · ... • a proof, in [4], that Khovanov's categorification, [12], of the reduced, n-colored Jones polynomial detects the unknot whenever n ≥ 2, as well as • a new method, due to... atascosa rural waterWebKhovanov homology is an unknot-detector May 2010 arXiv Authors: P. B. Kronheimer Tomasz S. Mrowka Massachusetts Institute of Technology Abstract and Figures We … atasehir restaurantsWeb9 feb. 2024 · Our definition of marking was chosen to coincide with the markings that arise in link Floer homology. In order to deal with complications arising from certain isotopes, we define three equivalences for marked surfaces and work over an equivalence class of marked surfaces when proving our generalization of Carter and Saito’s movie theorem. atascadero meat marketWebAs a bigraded theory, Khovanov homology therefore detects each of T+ and T−. One should not expect similar results for other knots in general, since for example Khovanov homology does not distinguish the knots 1022 and 1035 from each other. Like Kronheimer and Mrowka’s unknot detection result, Theorem 1.3 relies on a relationship atasan supervisor adalahWeb10 feb. 2015 · The singular instanton Floer homology was defined by Kronheimer and Mrowka in connection with their proof that the Khovanov homology is an unknot detector. We study this theory for knots and two-component links using equivariant gauge theory on their double branched covers. ataserti game kino qartuladWebWe prove that Khovanov homology with coefficients in Z/2Z detects the (2, 5) torus knot. Our proof makes use of a wide range of deep tools in Floer homology, Khovanov … atasehir turkeyWebKhovanov homology is a richer link invariant that categorifies the Jones polynomial. Using spectral sequences, we obtain a skein-type relation satisfied by the Khovanov … atash 17