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We establish some relationships between the meridional number, an invariant of links in the solid torus, and the expression of these links in various skein modules of the solid torus. As an application, we calculate the meridional number of a family of links, the Bing links.
Abstract—The celebrated Smale–Hirsch classification of immersions,allows one to obtain sev- eral nice applications of algebraic topology to differential topology. Unfortunately, these appli- cations are still not presented,in books,or survey papers either in Russian or in English. The purpose,of this paper is to expose the most simple and fundament...
Various examples of immersed codimension 1 manifolds are studied from the viewpoint of possible combinations of the Euler characteristics of the submanifolds of multiple selfintersection points. A complete answer is given for the immersed 5-manifolds in the 6-dimensional Euclidean space. Relations are discussed with other constructions in different...
An invariant for embeddings of links into the solid torus, called the meridional number, is introduced. Techniques are developed which produce a lower estimate of the meridional number in the case when the given link can be expressed as a satellite of another link. Such estimates yield a sufficient condition for shrinkability of toroidal decomposit...