【摘要】
It is well-known that the Alexander polynomial of a fibered knot must be monic. But in general the converse is not true. In this talk, we introduce the universal L^2-torsion of a 3-manifold, an invariant defined in analogy with the classical torsion, but using tools from L^2-theory. We will show that this invariant detects fibered 3-manifolds. Moreover, we extend the definition of the universal L^2-torsion to taut sutured 3-manifolds and show that it detects product sutured manifolds.
