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RESEARCH BLOG 3/17/03 I went to Baton Rouge over the weekend for an AMS meeting. Das-
 

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 Kania-Bartoszynska talked about their
new "quantum invariants" of 3-manifolds (they have a preprint [1]).
They are motivated by trying to generalize the Turaev-Viro invariants
of 3-manifolds 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 6j-symbols, which can be thought
of as integer labels on the edges of a tetrahedron. Given a (possibly
ideal) triangulation of a 3-manifold and non-negative 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 2-skeleton normally (apparently a stu-
dent of Matveev had noticed this association before). They sum the
product of 6j-symbols (and some other terms) over all the tetrahedra

  

Source: Agol, Ian - Department of Mathematics, Statistics, and Computer Science, University of Illinois at Chicago

 

Collections: Mathematics