Strong Band sum and dichromatic invariants.
Bands, Tangles and linear Skein theory.
On constructions of generalized skein modules
Józef 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 is given, and the corresponding background is developed. The possible coloring of fields by elements of...
Frobenius algebras and skein modules of surfaces in 3-manifolds
For each (commutative) Frobenius algebra there is defined a skein module of surfaces embedded in a given 3-manifold and bounding a prescribed curve system in the boundary. The skein relations are local and generate the kernel of a certain natural extension of the corresponding topological quantum field theory. In particular the skein module of the 3-ball is isomorphic to the ground ring of the Frobenius algebra. We prove a presentation theorem for the skein module with generators incompressible...
Link bordism skein modules
We compute link bordism skein modules of colored oriented links in oriented 3-manifolds. A Hurewicz theorem relating link bordism and link homotopy skein modules is proved.
Deformation of string topology into homotopy skein modules.
Page 1