On constructions of generalized skein modules

On Constructions of Generalized Skein Modules

Jozef Przytycki introduced skein modules of 3-manifolds and skein deformation initiating algebraic topology based on knots. We discuss the generalized skein modules of Walker, defined by fields and local relations. Some results by Przytycki are proven in a more general setting of fields defined by decorated cell-complexes in manifolds. A construction of skein theory from embedded TQFT-functors ...

On the Kauffman Skein Modules

Abstract. Let k be a subring of the field of rational functions in α, s which contains α, s. Let M be a compact oriented 3-manifold, and let K(M) denote the Kauffman skein module of M over k. Then K(M) is the free k-module generated by isotopy classes of framed links in M modulo the Kauffman skein relations. In the case of k = Q(α, s), the field of rational functions in α, s, we give a basis fo...

on direct sums of baer modules

the notion of baer modules was defined recently

Skein Modules of 3-manifolds

It is natural to try to place the new polynomial invariants of links in algebraic topology (e.g. to try to interpret them using homology or homotopy groups). However, one can think that these new polynomial invariants are byproducts of a new more delicate algebraic invariant of 3-manifolds which measures the obstruction to isotopy of links (which are homotopic). We propose such an algebraic inv...

Generalized Derivations on Modules