14,614 research outputs found
Twisted Reidemeister torsion, the Thurston norm and fibered manifolds
We prove that the twisted Reidemeister torsion of a 3-manifold corresponding
to a fibered class is monic and we show that it gives lower bounds on the
Thurston norm. The former fixes a flawed proof in [FV10], the latter gives a
quick alternative argument for the main theorem of [FK06].Comment: 11 pages, 1 figur
Novikov homology and noncommutative Alexander polynomials
In the early 2000's Cochran and Harvey introduced non-commutative Alexander
polynomials for 3-manifolds. Their degrees give strong lower bounds on the
Thurston norm. In this paper we make the case that the vanishing of a certain
Novikov-Sikorav homology module is the correct notion of a monic
non-commutative Alexander polynomial. Furthermore we will use the opportunity
to give new proofs of several statements about Novikov-Sikorav homology in the
three-dimensional context.Comment: 30 pages, to appear in a special volume of JKTR in memory of Tim
Cochra
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