Skein modules of 3-manifolds

Abstract

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 invariant based on skein theory introduced by Conway (1969) and developed by Giller (1982) as well as Lickorish and Millett (1987). (This is the first paper I wrote about skein modules, almost 20 years ago. The recent survey of skein modules is available at http://arxiv.org/abs/math.GT/0602264.)

11 pages, 13 figures; e-print prepared by Radmila Sazdanovic

Cited by in corpus (12)

• A positive basis for surface skein algebras
• Invariants of 4-manifolds from Khovanov-Rozansky link homology
• Strong positivity for the skein algebras of the $4$-punctured sphere and of the $1$-punctured torus
• Infinite families of hyperbolic $3$-manifolds with finite dimensional skein modules
• An invariant for colored bonded knots
• Iterated torus knots and double affine Hecke algebras
• Skein Modules and Lattice Gauge Field Theory
• On framings of links in 3-manifolds
• Kauffman bracket skein modules of small 3-manifolds
• Branes and DAHA Representations
• Trace Diagrams, Matrix Minors, and Determinant Identities
• Quantizing Derived Mapping Stacks