Doug Bullock

UNDERSTANDING THE KAUFFMAN BRACKET SKEIN MODULE

The Kauffman bracket skein module K(M) of a 3-manifold M is defined over formal power series in the variable h by letting A = eh/4. For a compact oriented surface F, it is shown that K(F×I) is a quantization of the -characters of the fundamental group of F corresponding to a geometrically defined Poisson bracket. Finite type invariants for unoriented knots and links are defined and obtained from topologically free Kauffman bracket modules. A structure theorem for K(M) is given in terms of the affine -characters of π1(M). It follows for compact M that K(M) can be generated as a module by cables on a finite set of knots. Moreover, if M contains no incompressible surfaces, the module is topologically finitely generated.

A finite set of generators for the Kauffman bracket skein algebra

Abstract. If F is a compact orientable surface it is known that the Kauffman bracket skein module of

THE (2, ∞)-SKEIN MODULE OF THE COMPLEMENT OF A (2, 2p+1) TORUS KNOT

F \times I

The Kauffman bracket skein module of a twist knot exterior

has a multiplicative structure. Our central result is the construction of a finite set of knots which generate the module as an algebra. We can then define an integer valued invariant of compact orientable 3-manifolds which characterizes

TOPOLOGICAL INTERPRETATIONS OF LATTICE GAUGE FIELD THEORY

S^3

The Kauffman bracket skein as an algebra of observables

.

Estimating the states of the Kauffman bracket skein module

In this paper we extend the list of three manifolds for which the (2, ∞)-skein module is known by giving the first explicit calculations for non-trivial knot exteriors. We show that for the complement of a (2, 2p+1) torus knot the module is free with a very simple basis. As a consequence, we obtain a family of polynomial invariants for links in these manifolds. The invariants are analogous to the Jones polynomial for links in S3.

Skein quantization and lattice gauge field theory

We compute the Kauffman bracket skein module of the comple- ment of a twist knot, finding that it is free and infinite dimensional. The basis consists of cables of a two-component link, one component of which is a meridian of the knot. The cabling of the meridian can be arbitrarily large while the cabling of the other component is limited to the number of twists. AMS Classification 57M27; 57M99

Assessing the STEM landscape: the current instructional climate survey and the evidence-based instructional practices adoption scale

Abstract:We construct lattice gauge field theory based on a quantum group on a lattice of dimension one. Innovations include a coalgebra structure on the connections and an investigation of connections that are not distinguishable by observables. We prove that when the quantum group is a deformation of a connected algebraic group G (over the complex numbers), then the algebra of observables forms a deformation quantization of the ring of

Skein related links in 3-manifolds

G