 
Summary: RESEARCH BLOG 3/17/03
I went to Baton Rouge over the weekend for an AMS meeting. Das
bach, Gilmer, and Litherland organized a special session on low
dimensional topology . Given their interests, there were many talks
about quantum invariants and knot theory. I'll try to discuss what
little I can recall or what I can comment on. See the abstracts at the
link above for a more comprehensive picture of range of talks given.
Charles Frohman and Joanna KaniaBartoszynska talked about their
new "quantum invariants" of 3manifolds (they have a preprint [1]).
They are motivated by trying to generalize the TuraevViro invariants
of 3manifolds away from roots of unity, which are state sums depend
ing on a complex parameter t, which is only finite if t is a root of
unity. The terms are defined by 6jsymbols, which can be thought
of as integer labels on the edges of a tetrahedron. Given a (possibly
ideal) triangulation of a 3manifold and nonnegative integers assigned
to each edge, they must satisfy the triangle inequality around each tri
angle and every sum is even, which means that the weights give rise to
a surface which intersects the 2skeleton normally (apparently a stu
dent of Matveev had noticed this association before). They sum the
product of 6jsymbols (and some other terms) over all the tetrahedra
