相关论文: From Heegaard diagrams to surgery

Lenses are a mathematical structure for maintaining consistency between a pair of systems. In their ongoing research program, Johnson and Rosebrugh have sought to unify the treatment of symmetric lenses with spans of asymmetric lenses. This…

The presented material is devoted to the equivalent conversion from the vertex graphs to the edge graphs. We suggest that the proved theorems solve the problem of the isomorphism of graphs, the problem of the graph's enumeration with the…

The Gauss self-linking integral of an unframed knot is not a knot invariant, but it can be turned into an invariant by adding a correction term which requires adding extra structure to the knot. We collect the different…

We introduce a simple combinatorial method for computing all versions of the knot Floer homology of the preimage of a two-bridge knot K(p,q) inside its double-branched cover, -L(p,q). The 4-pointed genus 1 Heegaard diagram we obtain looks…

In this paper we introduce and investigate the notions of diagrams and discrete extensions in the study of finitary $2$-representations of finitary $2$-categories.

We introduce a new very large family of transformations of rectangular diagrams of links that preserve the isotopy class of the link. We provide an example when two diagrams of the same complexity are related by such a transformation and…

We give invariants of pairs $(M,L)$ consisting of a closed connected oriented three-manifold and an (oriented) framed link $L$ embedded in $M$. This invariant generalizes the Kuperberg and Hennings-Kauffman-Radford (HKR) invariants of…

We introduce the multiplexing of a crossing, replacing a classical crossing of a virtual link diagram with multiple crossings which is a mixture of classical and virtual. For integers $m_{i}$ $(i=1,\ldots,n)$ and an ordered $n$-component…

In this paper we develop a structure called Link Algebra, in which we present a Set with two binary operations and an axiom system developed from the study of graph theory and set/antiset theory, sowing main theorems and definitions. Once…

In the graphical calculus of planar string diagrams, equality is generated by exchange moves, which swap the heights of adjacent vertices. We show that left- and right-handed exchanges each give strongly normalizing rewrite strategies for…

A branched covering map of surfaces induces a map in the opposite direction between their arc complexes. We represent a branched covering map combinatorially using what we call a lifting picture, and use this representation to computably…

We give an analysis of defeasible inheritance diagrams, also from the perspective of reactive diagrams.

In this paper, we introduce a new approach for drawing diagrams that have applications in software visualization. Our approach is to use a technique we call confluent drawing for visualizing non-planar diagrams in a planar way. This…

Let G be an arbitrary finite weighted digraph with weights in the set of complex rational functions. A general procedure is proposed which allows for the reduction of G to a smaller graph with a less complicated structure having the same…

Some problems related to the structure of higher terms of the epsilon-expansion of Feynman diagrams are discussed.

THIS PAPER IS NOW DEFUNCT: Check out "Graph Embeddings via Tensor Products and Approximately Orthonormal Codes", where it has been combined into one paper.

Given an special type of triangulation $T$ for an oriented closed 3-manifold $M^3$ we produce a framed link in $S^3$ which induces the same $M^3$ by an algorithm of complexity $O(n^2)$ where $n$ is the number of tetrahedra in $T$ . The…

We provide an intergral lift of the combinatorial definition of Heegaard Floer homology for nice diagrams, and show that the proof of independence using convenient diagrams adapts to this setting.

In this paper we review the definitions of homogeneous and alternative links. We also give two new characterizations of an alternative link diagram, one within the context of the enhanced checkerboard graph and another from the labeled…

We establish an embedding from the Hecke algebra associated with the edge contraction of a Coxeter system along an edge to the Hecke algebra associated with the original Coxeter system.