相关论文: A classification of transitive links and periodic …
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…
We study framed links in irreducible 3-manifolds that are $Z$-homology 3-spheres or atoroidal $Q$-homology 3-spheres. We calculate the dual of the Kauffman skein module over the ring of two variable power series with complex coefficients.…
We give a concise proof of a classification of lens spaces up to orientation-preserving homeomorphisms. The chief ingredient in our proof is a study of the Alexander polynomial of ` symmetric' links in $S^3$.
We study Vassiliev invariants of links in a 3-manifold $M$ by using chord diagrams labeled by elements of the fundamental group of $M$. We construct universal Vassiliev invariants of links in $M$, where $M=P^2\times [0,1]$ is a cylinder…
Let $L$ be an alternating prime non-split link in $S^3$. We use the category of flypes between reduced alternating diagrams for $L$ to classify involutions on $L$. As consequences, we show that the quotient of an alternating periodic link…
We give a congruence relating a one variable specialization of the two variable Kauffman polynomial of any periodic link to that of its mirror image. Consequently, we obtain a new and simple criterion for periodicity of links.
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 $F \times I$…
We construct a polynomial invariant, for links in a Seifert fibered or atoroidal rational homology 3-sphere, which generalizes the 2-variable Jones polynomial (HOMFLY). As a consequence, we show that the dual of the HOMFLY skein module of a…
Triple linking numbers were defined for 3-component oriented surface-links in 4-space using signed triple points on projections in 3-space. In this paper we give an algebraic formulation using intersections of homology classes (or cup…
In this work, we study the interlace polynomial as a generalization of a graph invariant to delta-matroids. We prove that the interlace polynomial satisfies the four-term relation for delta-matroids and determines thus a finite type…
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 use the skein theory of $\mathfrak{sl}_3$-webs to study the properties of the quantum $\mathfrak{sl}_3$-link polynomial of positive links. We give explicit formulae for the three leading terms of the polynomial on positive links in terms…
We construct a link in the $3$-space that is not isotopic to any PL link (non-ambiently). In fact, there exist uncountably many $I$-equivalence classes of links. The paper also includes some observations on Cochran's invariants $\beta_i$.
We study certain orientation-preserving involutions on three-dimensional small covers. We prove that the quotient space of an orientable three-dimensional small cover by such an involution in $\mathbb{Z}_2^3$ is homeomorphic to a connected…
Periodic tangles are 1-dimensional submanifolds in the 3-space with translational symmetry. In this paper, we define the linking numbers for singly, doubly, and triply periodic tangles using appropriate motifs and show that they are…
We introduce a homology surgery problem in dimension 3 which has the property that the vanishing of its algebraic obstruction leads to a canonical class of \pi-algebraically-split links in 3-manifolds with fundamental group \pi . Using this…
In this paper we construct new classes of mixed singularities that provide realizations of real algebraic links in the $3$-sphere. Classifications and characterizations of real algebraic links are still open. These new classes of mixed…
In this paper we introduce the definition of transitivity for oriented 3-hypergraphs in order to study partial and complete cyclic orders. This definition allow us to give sufficient conditions on a partial cyclic order to be totally…
In this paper, we give an isotopy classification of 3-bridge spheres of 3-bridge arborescent links, which are not Montesinos links. To this end, we prove a certain refinement of a theorem of J.S. Birman and H.M. Hilden on the relation…
We give criteria for framed links and 3-manifolds to be periodic of prime order. As applications we show that the Poincare sphere is of periodicity 2, 3, 5 only and the Brieskorn sphere (2,3,7) is of periodicity 2, 3, 7 only.