ﻻ يوجد ملخص باللغة العربية
The following is an amalgamation of four preprints and some computer programs which together represent the current state of our investigations of higher order links. This investigation was motivated by questions discussed and raised in the first authors paper New States of Matter Suggested by New Topological Structures. An important motivation has been to suggest the synthesis of new types of molecules (see the relevant articles listed in the bibliography). This discussion is not final, but we think that the results and methods are worth making public and would be useful for other investigators.
In the present work, we realize the space of string 2-links $mathcal{L}$ as a free algebra over a colored operad denoted $mathcal{SCL}$ (for Swiss-Cheese for links). This result extends works of Burke and Koytcheff about the quotient of $mathcal{L}$
We study configuration space integral formulas for Milnors homotopy link invariants, showing that they are in correspondence with certain linear combinations of trivalent trees. Our proof is essentially a combinatorial analysis of a certain space of
Configuration space integrals have in recent years been used for studying the cohomology of spaces of (string) knots and links in $mathbb{R}^n$ for $n>3$ since they provide a map from a certain differential algebra of diagrams to the deRham complex o
In this paper we give a simple proof of the equivalence between the rational link associated to the continued fraction $left[ a_{1},a_{2},cdots a_{m}right],$ $a_{i}inmathbb{N}$, and the two bridge link of type $p/q,$ where $p/q$ is the rational given
With the idea of an eventual classification of 3-bridge links, we define a very nice class of 3-balls (called butterflies) with faces identified by pairs, such that the identification space is $S^{3},$ and the image of a prefered set of edges is a li