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3-Manifold Groups
We summarize properties of 3-manifold groups, with a particular focus on the consequences of the recent results of Ian Agol, Jeremy Kahn, Vladimir Markovic and Dani Wise.
Twisted Alexander Polynomials of Hyperbolic Knots
We study a twisted Alexander polynomial naturally associated to a hyperbolic knot in an integer homology 3-sphere via a lift of the holonomy representation. Expand
The cobordism group of homology cylinders
Abstract Garoufalidis and Levine introduced the homology cobordism group of homology cylinders over a surface. This group can be regarded as an enlargement of the mapping class group. Using torsionExpand
Eta invariants as sliceness obstructions and their relation to Casson-Gordon invariants
We give a useful classification of the metabelian unitary repre- sentations of π1(MK), where MK is the result of zero-surgery along a knot K ⊂ S 3 . We show that certain eta invariants associated toExpand
3-manifold groups are virtually residually p
Given a prime $p$, a group is called residually $p$ if the intersection of its $p$-power index normal subgroups is trivial. A group is called virtually residually $p$ if it has a finite indexExpand
We give a short introduction to the theory of twisted Alexander polynomials of a 3-manifold associated to a representation of its fundamental group. We summarize their formal properties and weExpand
Twisted Alexander polynomials detect fibered 3-manifolds
A classical result in knot theory says that the Alexander polynomial of a fibered knot is monic and that its degree equals twice the genus of the knot. This result has been generalized by variousExpand
The profinite completion of $3$-manifold groups, fiberedness and the Thurston norm
We show that a regular isomorphism of profinite completion of the fundamental groups of two 3-manifolds N1 and N2 induces an isometry of the Thurston norms and a bijection between the fiberedExpand
New Constructions of Slice Links
We use techniques of Freedman and Teichner to prove that, under certain circumstances, the multi-infection of a slice link is again slice (not necessarily smoothly slice). We provide a generalExpand
The Thurston norm, fibered manifolds and twisted Alexander polynomials
Abstract Every element in the first cohomology group of a 3-manifold is dual to embedded surfaces. The Thurston norm measures the minimal ‘complexity’ of such surfaces. For instance the Thurston normExpand