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 … 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 …

A generalized skein relation for Khovanov homology and a ...

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 … WebKhovanov homology is a richer link invariant that categorifies the Jones polynomial. Using spectral sequences, we obtain a skein-type relation satisfied by the Khovanov … the hound of the baskervilles film

Khovanov homology is an unknot-detector : P. B. Kronheimer : …

WebAs 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 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 … 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 ... the hound of the baskervilles play script pdf