Jérôme Dubois
A Euclidean geometric invariant of framed (un)knots in manifolds.
Wed, 02/24/2010 - 16:01 — SomNambulAuthors: Jérôme Dubois, Igor G. Korepanov, Evgeniy V. Martyushev
Subjects: Geometric Topology
AbstractWe present an invariant of a three-dimensional manifold with a framed knot in
it based on the Reidemeister torsion of an acyclic complex of Euclidean
geometric origin. To show its nontriviality, we calculate the invariant for
some framed (un)knots in lens spaces. Our invariant is related to a
finite-dimensional fermionic topological quantum field theory.Multivariable Twisted Alexander Polynomial for hyperbolic three-manifolds with boundary.
Tue, 08/25/2009 - 22:41 — SomNambulAuthors: Jérôme Dubois, Yoshikazu Yamaguchi
Subjects: Geometric Topology
AbstractWe consider a sign-determined Reidemeister torsion with multivariables for a
hyperbolic three-dimensional manifold with cusps. Using a cut and paste
argument, we prove that this Reidemeister torsion is a polynomial invariant
when provided with appropriate conditions on the topology of the manifold and
SL(2, C)-representations of its fundamental group. Under such assumptions, it
is proved that this polynomial invariant is reciprocal like the usual Alexander
polynomial.
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