### KNOTS in WASHINGTON II

The Second Miniconference on Knot Theory and its Ramifications
will be held on Saturday, March 30, 1996 at the George
Washington University.

10:30 - 11:30   Ken Millett, Physical Knots
Abstract. I would discuss results on polygonal knots, knot energies,
and thickness of knots.

12:00 -  1:00   Jeff Weeks, What is a hyperbolic knot?
Abstract.
The talk will give a gentle introduction to the theory
of hyperbolic knots.  The computer program SnapPea will
illustrate the main ideas.

2:30 -  3:30  Wilbur Whitten, Knot inversion and the isometry groups
of hyperbolic 3-manifolds
Abstract:
The problem of deciding whether a given knot K in the 3-sphere is
invertible is shown to be equivalent to deciding when two knot groups are
isomorphic.  These are the groups
of two satellite knots formed with K as their (only) maximal companion, and
each of these satellite knots is itself noninvertible regardless of the
invertibility status of K.  This result shows clearly why the invertibility
question of a knot is generally so difficult and it coincidently leads to
three conjectures (too lengthy to include in this abstract)
concerning ths isometry groups of the hyperbolic 3-manifolds obtained
by surgery on hyperbolic links.  If these conjectures are correct, such
an isometry group would be one of a well-defined finite collection.

3:45 -  4:10  Yongwu Rong, Introduction to Higher Order Link Polynomials
Abstract:
Two major link invariants are Homfly+PT polynomial
and the Vassiliev invariants.  We introduce what we call higher
order link polynomials'' that combine ingredients from both.
We carry out a detailed study for the order one polynomials.
Various possible applications will be discussed.

4:20 -  4:45  Jozef H. Przytycki, What is new in skein modules?
Abstract:
Skein modules are the basic objects of algebraic topology based on knots
(as homology and homotopy groups are the basic objects of a classical
algebraic topology). The last half a year brought big progress in the
theory (which is 9 years old). It will be illustrated by an example
of detecting torsion in the Kauffman bracket skein modules using
an SL(2,C) character variety and hyperbolic geometry.

4:55 -  5:20  Adam Sikora, Skein algebra of a handlebody from the
point of view of algebraic geometry
Abstract:
This talk will be mainly concerned with a non-standard 'algebraic topology'
built on knots. In particular, we will define {\it the Kauffman bracket skein
module} $S(M)$, a module associated to any 3-dimensional manifold $M$.
A particular version of this module has a structure of a commutative algebra
and therefore it is called a {\it skein algebra}. The skein algebra depends
only on the fundamental group of a manifold.
We are going to investigate skein algebras using methods of algebraic
geometry. In particular, we will show how the skein algebra associated to a
manifold $M$ is connected with a {\it character variety}, an algebraic set
representing all traces of homomorphisms of $\pi_1(M)$ into $Sl_2(C)$.
This will give a very nice geometric interpretation of character varieties,
which essentially have been investigated since the time of Poincare, Fricke
and Klein.

5:30 - 5:50   Michael McDaniel, Cablings of Vassiliev Invariants
Abstract:
We will study Vassiliev Invariants coming form cabling and
describe a practical way of calculating them.

Local Organizers: Jozef H. Przytycki e-mail: przytyck@math.gwu.edu
Yongwu Rong        e-mail: rong@math.gwu.edu