Related papers: A link invariant with values in the Witt ring
For a classical link, Milnor defined a family of isotopy invariants, called Milnor $\overline{\mu}$-invariants. Recently, Chrisman extended Milnor $\overline{\mu}$-invariants to welded links by a topological approach. The aim of this paper…
Pulling back the weight system associated with the spinor representation of the Lie algebra so(7) by the universal Vassiliev-Kontsevich invariant yields a numerical link invariant with values in formal power series. Computing some skein…
We introduce new topological quantum invariants of compact oriented 3-manifolds with boundary where the boundary is a disjoint union of two identical surfaces. The invariants are constructed via surgery on manifolds of the form $F \times I$…
A group invariant for links in thickened closed orientable surfaces is studied. Associated polynomial invariants are defined. The group detects nontriviality of a virtual link and determines its virtual genus.
Based on the notion of a $\Delta$-group(oid), ring-valued invariants of pairs of topological spaces can be defined in intrinsic topological terms.
It is known that the writhe calculated from any reduced alternating link diagram of the same (alternating) link has the same value. That is, it is a link invariant if we restrict ourselves to reduced alternating link diagrams. This is due…
Based on the analogy between knots and primes, J. Hillman, D. Matei and M. Morishita defined the Iwasawa invariants for sequences of cyclic covers of links with an analogue of Iwasawa's class number formula of number fields. In this paper,…
To each link $L$ in $S^3$ we associate a collection of certain labelled directed trees, called width trees. We interpret some classical and new topological link invariants in terms of these width trees and show how the geometric structure…
This paper generalize [7](math.GT/0601291): We construct new links invariants from g, a type I basic classical Lie superalgebra. The construction uses the existence of an unexpected replacement of the vanishing quantum dimension of typical…
In this paper we introduce two theories of finite type invariants for framed links with fixed linking matrix. We show that these thepries are related to the theory of Vassiliev invariants of framed links. We also study the corresponding…
In this paper we construct a multivariable link invariant arising from the quantum group associated to the special linear Lie superalgebra sl(2|1). The usual quantum group invariant of links associated to (generic) representations of…
We extend several classical invariants of links in the 3-sphere to links in so-called quasi-cylinders. These invariants include the linking number, the Seifert form, the Alexander module, the Alexander-Conway polynomial and the…
This paper introduces a novel approach to the axiomatic theory of quadratic forms. We work internally in a category of certain partially ordered sets, subject to additional conditions which amount to a strong form of local presentability.…
Using the symplectic geometry of certain manifolds which appear naturally in Lie theory, we define an invariant which assigns a graded abelian group to an oriented link. The relevant manifolds are transverse slices to certain nilpotent…
This paper is expository and is accessible to students. We define simple invariants of knots or links (linking number, Arf-Casson invariants and Alexander-Conway polynomials) motivated by interesting results whose statements are accessible…
We consider certain invariants of links in 3-manifolds, obtained by a specialization of the Turaev-Viro invariants of 3-manifolds, that we call colored Turaev-Viro invariants. Their construction is based on a presentation of a pair (M,L),…
We review the recent developments of quantum invariants of 3-manifolds and links: $\hat{Z}$ and $F_L$. They are $q$-series invariants originated from mathematical physics. They exhibit rich features, for example, quantum modularity,…
Taking as starting point a perturbative study of the classical equations of motion of the non-Abelian Chern-Simons Theory with non-dynamical sources, we search for analytical expressions for link invarians. In order to present these…
We define invariants for a framed link equipped with a SL2 local system in its complement and additional combinatorial data based on the theory of representations of stated skein algebras at roots of unity of punctured bigons and the…
The usual construction of link invariants from quantum groups applied to the superalgebra D_{2 1,alpha} is shown to be trivial. One can modify this construction to get a two variable invariant. Unusually, this invariant is additive with…