相关论文: Finite Type Link Homotopy Invariants
In this paper we define the 1,2-coloured HOMFLY-PT link homology and prove that it is a link invariant. We conjecture that this homology categorifies the coloured HOMFLY-PT polynomial for links whose components are labelled 1 or 2.
The Hom complex ${\rm Hom}(T,G)$ of graphs is a CW-complex associated to a pair of graphs $T$ and $G$, considered in the graph coloring problem. It is known that certain homotopy invariants of ${\rm Hom}(T,G)$ give lower bounds for the…
New invariants of links are constructed using the skein invariant polynomial of colored links defined by the author in [1]. These invariants are stronger than the homflypt polynomial.
We define a new finite type invariant for stably homeomorphic class of curves on compact oriented surfaces without boundaries and extend to a regular homotopy invariant for spherical curves.
We initiate the study of classical knots through the homotopy class of the n-th evaluation map of the knot, which is the induced map on the compactified n-point configuration space. Sending a knot to its n-th evaluation map realizes the…
We extend the notion of intersection graphs for knots in the theory of finite type invariants to string links. We use our definition to develop weight systems for string links via the adjacency matrix of the intersection graph, and show…
This paper defines an invariant associated to Whitehead's certain exact sequence of a simply connected CW-complex which is much more elementary - and less powerful - than the boundary invariant of Baues. Nevertheless, in good cases, it…
In this paper, we define finite type invariants for cyclic equivalence classes of nanophrases and construct the universal ones. Also, we identify the universal finite type invariant of degree 1 essentially with the linking matrix. It is…
We define a Khovanov homotopy type for $sl_2(\mathbb{C})$ colored links and quantum spin networks and derive some of its basic properties. In the case of $n$-colored B-adequate links, we show a stabilization of the homotopy types as the…
There exists a simplified Bar-Natan Khovanov complex for open 2-braids. The Khovanov cohomology of a knot diagram made by gluing tangles of this type is therefore often amenable to calculation. We lift this idea to the level of the…
We establish a direct map between refined topological vertex and sl(N) homological invariants of the of Hopf link, which include Khovanov-Rozansky homology as a special case. This relation provides an exact answer for homological invariants…
Given a link map f into a manifold of the form Q = N \times \Bbb R, when can it be deformed to an unlinked position (in some sense, e.g. where its components map to disjoint \Bbb R-levels) ? Using the language of normal bordism theory as…
We explore a family of invariants obtained from linking numbers. This is a family of Kauffman finite type invariants.
We introduce new skein invariants of links based on a procedure where we first apply the skein relation only to crossings of distinct components, so as to produce collections of unlinked knots. We then evaluate the resulting knots using a…
This paper studies rotational virtual knot theory and its relationship with quantum link invariants. Every quantum link invariant for classical knots and links extends to an invariant of rotational virtual knots and links. The paper sets up…
We introduce notions of {\it upper chernrank} and {\it even cup length} of a finite connected CW-complex and prove that {\it upper chernrank} is a homotopy invariant. It turns out that determination of {\it upper chernrank} of a space $X$…
In previous work, we defined the intersection graph of a chord diagram associated with a string link (as in the theory of finite type invariants). In this paper, we look at the case when this graph is a tree, and we show that in many cases…
This paper identifies a new class of shape invariant models. These models are based on extensions of conventional quantum mechanics that satisfy a string-motivated minimal length uncertainty relation. An important feature of our…
In this paper, we introduce Bar-Natan homology for null homologous links in \mathbb{RP}^3 over the field of two elements. It is a deformation of the Khovanov homology in \mathbb{RP}^3 defined by Asaeda, Przytycki and Sikora. We also define…
This paper continues the study of finite-type invariants of homology spheres studied by Ohtsuki and Garoufalidis. We apply the surgery classification of links to give a diagrammatic description, using ideas of Ohtsuki. This uses a…