Websimple invariant wSL of genus one knots in Z-spheres in Section 1.3. As we show in Theo-rem 1.12, this second invariant wSL is a combination of wδ and a (degree 3) knot invariant w3, which appears in a surgery formula for a (degree 2) invariant of Q-spheres. To prove the WebApr 23, 2024 · These operators are parameterized in one variable, and the trace happens to be a polynomial function in that variable -- hence, a polynomial invariant of knots. Kauffman was able to quickly use the point of view he developed in Formal Knot Theory to come up with the Kauffman bracket, a graphical calculus for computing Jones polynomials. It ...
Knot theory - Cornell University
WebJan 15, 2012 · Although, in my opinion, it is strongly influenced by Rolfsen's Knots and Links, Prasolov and Sossinsky's Knots, Links, Braids and 3-Manifolds: An Introduction to the New Invariants in Low-Dimensional Topology is nice because there are references to recent articles in the appendices of each section. WebTrisection invariants of 4-manifolds from Hopf algebras - Xingshan CUI 崔星山, Purdue (2024-10-25) The Kuperberg invariant is a topological invariant of closed 3-manifolds based on finite-dimensional Hopf algebras. Here we initiate the program of constructing 4-manifold invariants in the spirit of Kuperberg's 3-manifold invariant. milestone albury
On elementary invariants of genus one knots and Seifert …
WebA function on knot diagrams which assigns the same value to all representatives of a knot is called a knot invariant. Knot theorists say that some invariant fdominates gif there exists a pair of knots K 1 and K 2 such that g(K 1) = g(K 2), but f(K 1) 6= f(K 2). This inequality is proof that K 1 and K 2 are not isomorphic, and this is how knot ... WebVectorized Knot Homology Polynomial Invariants (click to view) KH Red Q Vector. KH Red Mod2 Vector. KH Odd Red Q Vector. KH Odd Red Mod2 Vector. HFK Polyomial Vector. Hyperbolic Invariants. Submit. Chern-Simons Invariant. WebNov 10, 2024 · Yes, however they are not known to be computable in polynomial time. A quick an incomplete survey: The Seifert genus of a knot is 0 if and only if it is unknotted. … milestone air reviews florida