搜索结果: 1-7 共查到“几何拓扑学 Knot”相关记录7条 . 查询时间(0.173 秒)
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...
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...