搜索结果: 1-15 共查到“数学 knot”相关记录21条 . 查询时间(0.058 秒)
Jones polynomial and knot transitions in Hermitian and non-Hermitian topological semimetals
Hermitian Topological semimetal Junction Transition
2023/1/4
Topological nodal line semimetals can host stable chained, linked, or knotted line degeneracies in momentum space protected by symmetries. In this talk, I will show how to use the Jones polynomial (wh...
In this thesis, we give a topological interpretation of knot contact homology, by considering intersections of a particular class of chains of open strings with the knot itself. In doing so, we provid...
Abstract: The state of a knot is defined in the realm of Chern-Simons topological quantum field theory as a holomorphic section on the SU(2) character manifold of the peripheral torus. We compute the ...
Computing the crosscap number of a knot using integer programming and normal surfaces
integer programming normal surfaces crosscap number of a knot Geometric Topology
2011/9/5
Abstract: The crosscap number of a knot is an invariant describing the non-orientable surface of smallest genus that the knot bounds. Unlike knot genus (its orientable counterpart), crosscap numbers a...
A rank inequality for the knot Floer homology of double branched covers
the knot Floer homology double branched covers Geometric Topology
2011/9/1
Abstract: Given a knot $K$ in $S^3$, let $\Sigma(K)$ be the double branched cover of $S^3$ over $K$. We show there is a spectral sequence whose $E^1$ page is $(\hat{HFK}(\Sigma(K), K) \otimes V^{n-1})...
Knot Polynomials: Myths and Reality
Alexander polynomial Jones polynomial Homflypt polynomial Khovanov polynomial Kauffman polynomial factorizabitity primeness
2011/8/31
Abstract: This article provides an overview of relative strengths of polynomial invariants of knots and links, such as the Alexander, Jones, Homflypt, and Kaufman two-variable polynomial, Khovanov hom...
Constructing a broken Lefschetz fibration of S^4 with a spun or twist-spun torus knot fiber
broken Lefschetz fibration twist-spun torus knot fiber Algebraic Topology
2011/8/31
Abstract: Much work has been done on the existence and uniqueness of broken Lefschetz fibrations such as those by Auroux et al., Gay and Kirby, Lekili, Akbulut and Karakurt, Baykur, and Williams, but ...
Knot state asymptotics II, Witten conjecture and irreducible representations
Knot state asymptotics II Witten conjecture irreducible representations Geometric Topology
2011/8/30
Abstract: This article pursues the study of the knot state asymptotics in the large level limit initiated in "Knot sate Asymptotics I". As a main result, we prove the Witten asymptotic expansion conje...
Knot state asymptotics I, AJ Conjecture and abelian representations
Knot state asymptotics I AJ Conjecture abelian representations Geometric Topology
2011/8/30
Abstract: Consider the Chern-Simons topological quantum field theory with gauge group SU(2) and level k. Given a knot in the 3-sphere, this theory associates to the knot exterior an element in a vecto...
Combinatorial knot Floer homology and cyclic double branched covers
Combinatorial knot Floer homology cyclic double branched covers Geometric Topology
2011/8/26
Abstract: Using a Heegaard diagram for the pullback of a knot $K \subset S^3$ in its cyclic double branched cover $\Sigma_2(K)$, we give a combinatorial proof for the invariance of knot Floer homology...
The Least Spanning Area of a Knot and the Optimal Bounding Chain Problem
Least Spanning Area Knot Optimal Bounding Chain Problem
2011/3/2
Two fundamental objects in knot theory are the minimal genus surface and the least area surface bounded by a knot in a 3-dimensional manifold.
If K is a knot or link in R3 and S R3 is a smoothly embedded 2-sphere meeting K transversely in 4-points, then one can form a new knot or link K′ as follows. One cuts R3 along S and then glues the t...
Symmetries and adjunction inequalities for knot Floer homology
Symmetries adjunction inequalities knot Floer homology
2011/1/21
We derive symmetries and adjunction inequalities of the knot Floer homology groups which appear to be especially interesting for homologically essential knots.
Cofinitely Hopfian groups, open mappings and knot complements
Cofinitely Hopfian open mappings relatively hyperbolic
2011/1/19
A group is defined to be cofinitely Hopfian if every homomorphism → whose image is of finite index is an automorphism.Geometrically significant groups enjoying this pr...
Based on the proof of Labastida-Mari˜no-Ooguri-Vafa conjecture [6], we derive an infinite product formula for Chern-Simons partition functions, the generating function of quantum slN invariants. ...