The Homflypt skein module of a connected sum of 3-manifolds

  title={The Homflypt skein module of a connected sum of 3-manifolds},
  author={Patrick M. Gilmer and Jianyuan K. Zhong},
  journal={Algebraic \& Geometric Topology},
If M is an oriented 3-manifold, let S(M )d enote the Homf lypt skein module of M: We show that S (M 1#M 2) is isomorphic to S(M1) S(M2) modulo torsion. In fact, we show that S(M1#M2) is isomorphic to S(M1)S(M2) if we are working over a certain localized ring. We show the similar result holds for relative skein modules. If M contains a separating 2-sphere, we give conditions under which certain relative skein modules of M vanish over specied localized rings. 
The Kauffman skein module of a connected sum of 3-manifolds
The Yang-Mills Measure in the $SU(3)$ Skein Module
Let A be a nonzero complex number which is not a root of unity. Let F be a compact oriented surface, the SU(3)-skein space of F, SA(F), is the vector space over ℂ generated by framed oriented links
Homflypt skein theory, string topology and 2-categories
  • U. Kaiser
  • Mathematics
    Journal of Knot Theory and Its Ramifications
  • 2022
We show that relations in Homflypt type skein theory of an oriented [Formula: see text]-manifold [Formula: see text] are induced from a [Formula: see text]-groupoid defined from the fundamental
Deformation of Homotopy into Isotopy in Oriented 3-Manifolds
We will show that deformation quantization in skein theory of oriented 3-manifolds is induced from a topological deformation quantization of the fundamental 2-groupoid of the space of immersions of
HOMFLY-PT skein module of singular links in the three-sphere
For a ring $R$, we denote by $R[\mathcal L]$ the free $R$-module spanned by the isotopy classes of singular links in $\mathbb S^3$. Given two invertible elements $x,t \in R$, the HOMFLY-PT skein
The braid approach to the HOMFLYPT skein module of the lens spaces $L(p,1)$
In this paper we present recent results toward the computation of the HOMFLYPT skein module of the lens spaces $L(p,1)$, $\mathcal{S}\left(L(p,1) \right)$, via braids. Our starting point is the knot
Problems on invariants of knots and 3-manifolds
This is a list of open problems on invariants of knots and 3-manifolds with expositions of their history, background, significance, or importance. This list was made by editing open problems given in