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Morrison, Walker, and Wedrich used the blob complex to construct a generalization of Khovanov-Rozansky homology to links in the boundary of a 4-manifold. The degree zero part of their theory, called the skein lasagna module, admits an elementary definition in terms of certain diagrams in the 4-manifold. We give a description of the skein lasagna module for 4-manifolds without 1- and 3-handles, and present some explicit calculations for disk bundles over $S^2$.
Let $k$ be a subring of the field of rational functions in $x, v, s$ which contains $x^{pm 1}, v^{pm 1}, s^{pm 1}$. If $M$ is an oriented 3-manifold, let $S(M)$ denote the Homflypt skein module of $M$ over $k$. This is the free $k$-module generated b
The Hecke algebra H_n contains well known idempotents E_{lambda} which are indexed by Young diagrams with n cells. They were originally described by Gyoja. A skein theoretical description of E_{lambda} was given by Aiston and Morton. The closure of E
This paper is a brief overview of some of our recent results in collaboration with other authors. The cocycle invariants of classical knots and knotted surfaces are summarized, and some applications are presented.
An algebraic system is proposed that represent surface cobordisms in thickened surfaces. Module and comodule structures over Frobenius algebras are used for representing essential curves. The proposed structure gives a unified algebraic view of state
Three new knot invariants are defined using cocycles of the generalized quandle homology theory that was proposed by Andruskiewitsch and Gra~na. We specialize that theory to the case when there is a group action on the coefficients. First, quandle