Webtheory is the knot Floer homology HFK\(L) of Ozsvath-Szab´o and Rasmussen [7], [15]. In its simplest form, HFK\(L) is a bigraded vector space whose Euler characteristic is the Alexander polynomial. Knot Floer homology is known to detect the genus of a knot [10], as well as whether a knot is fibered [14]. There exists a refinement of HFK ... WebBy definition the canonical genus of a knot K gives an upper bound for the genus g(K) of K, that is the minimum of genera of all possible Seifert surfaces for K. In this paper, we introduce an operation, called the bridge-replacing move, for a knot diagram which does not change its representing knot type and does not increase the genus of the ...
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Webinvariants obstruct the knot from being concordant to a knot of lower genus. For another 59 knots we show an explicit concordance, illustrated in the appendix. This extends the … WebKnotted Roots On The Lake is a nature-inspired wedding venue in Land O Lakes, Florida. This stunning farm and garden space boasts a charming setting perfect for the bohemian … dylan by true grit tops
Knot Genus -- from Wolfram MathWorld
WebLet Kbe an alternating knot. It is well-known that one can detect from a minimal projection of Kmany topological invariants (such as the genus and the crossing number, see for instance [5], [17]) and many topological properties such as to be bered or not (see for instance [11]). Hence it is natural to raise about achirality WebExample: An example of a knot is the Unknot, or just a closed loop with no crossings, similar to a circle that can be found in gure 1. Another example is the trefoil knot, which has three crossings and is a very popular knot. The trefoil knot can be found in gure 2. Figure 1: Unknot Figure 2: Trefoil Knot WebBEHAVIOR OF KNOT INVARIANTS UNDER GENUS 2 MUTATION 3 Preserved by (2,0)-mutation Changed by (2,0)-mutation Hyperbolic volume/Gromov norm of the knot exterior HOMFLY-PT polynomial Alexander polynomial and generalized signature sl2-Khovanov Homology Colored Jones polynomial (for all colors) Table 1.2. Summary of known results … dylan cadiou