Related papers: A note on quasi-alternating Montesinos links
We construct explicitly the Khovanov homology theory for virtual links with arbitrary coefficients by using the twisted coefficients method. This method also works for constructing Khovanov homology for ``non-oriented virtual knots'' in the…
We introduce quasi-Gorenstein morphisms of commutative local dg-algebras and use a Gorenstein version of the virtually small property to characterize them, a result which is new even for homomorphisms of local rings. In a different…
The main goal of the present paper is to construct new invariants of knots with additional structure by adding new gradings to the Khovanov complex. The ideas given below work in the case of virtual knots, closed braids and some other cases…
We prove several criteria for quasi-isometry between non-locally-finite graphs and their structure trees. Results of M\"oller in \cite{moeller92ends2} for locally finite and transitive graphs are generalized. We also give a criterion which…
Using an involved study of the Jones polynomial, we determine, as our main result, the crossing numbers of (prime) amphicheiral knots. As further applications, we show that several classes of links, including semiadequate links and…
We define a variation of Khovanov homology with an explicit description in terms of the spanning trees of a link projection. We prove that this new theory is a link invariant and describe some of its properties. Finally, we provide some the…
We define a group-valued invariant of virtual knots and relate it to various other group-valued invariants of virtual knots, including the extended group of Silver-Williams and the quandle group of Manturov and Bardakov-Bellingeri. A…
A structure ${\mathbb Y}$ of a relational language $L$ is called almost chainable iff there are a finite set $F \subset Y$ and a linear order $<$ on the set $Y\setminus F$ such that for each partial automorphism $\varphi$ (i.e., local…
A (Hasse) diagram of a finite partially ordered set (poset) P will be called quasiplanar if for any two incomparable elements u and v, either v is on the left of all maximal chains containing u, or v is on the right of all these chains.…
Hybrid topologies on the real line have been studied by various authors. Among the hybrid spaces, there are also Hattori spaces. However, some of the hybrid spaces are not homeomorphic to Hattori spaces. In this article, a common…
Khovanov homology is a recently introduced invariant of oriented links in $\mathbb{R}^3$. It categorifies the Jones polynomial in the sense that the (graded) Euler characteristic of the Khovanov homology is a version of the Jones polynomial…
We consider Milnor invariants for certain covering links as a generalization of covering linkage invariants formulated by R. Hartley and K. Murasugi. A set of Milnor invariants for covering links is a cobordism invariant of a link, and that…
We consider generalizations of pairing relations for Kovalevskaya exponents in quasihomogeneous systems with quasihomogeneous tensor invariants. The case of presence of a Poisson structure in the system is investigated in more detail. We…
The Kauffman-Harary conjecture states that for any reduced alternating diagram K of a knot with a prime determinant p, every non-trivial Fox p-coloring of K assigns different colors to its arcs. We generalize the conjecture by stating it in…
In this paper we discuss, in terms of quivers with relations, sufficient and necessary conditions for an algebra to be a quasitilted algebra. We start with an algebra with global dimension two and we give a sufficient condition for it to be…
The construction of link polynomials associated with finite dimensional representations of ribbon quasi-Hopf algebras is discussed in terms of the formulation of an appropriate Markov trace. We then show that this Markov trace is invariant…
The splitting number of a link is the minimal number of crossing changes between different components required, on any diagram, to convert it to a split link. We introduce new techniques to compute the splitting number, involving covering…
Pseudo links are equivalence classes under Reidemeister-type moves of link diagrams containing crossings with undefined over and under information. In this paper, we extend the Kauffman bracket and Jones-type polynomials from planar pseudo…
This paper introduces the tensor representation of a network, here tensors are the primitive structures of the network. In view of tensor chains, two binary operations on tensor sets are defined: chain addition and reducing. Based on the…
Kashaev and Reshetikhin proposed a generalization of the Reshetikhin-Turaev link invariant construction to tangles with a flat connection in a principal G-bundle over the complement of the tangle. The purpose of this paper is to adapt and…