We establish results concerning the profinite completions of 3-manifold groups. In particular, we prove that the complement of the figure-eight knot SrK is distinguished from all other compact 3-manifolds by the set of finite quotients of its fundamental group. In addition, we show that if M is a compact 3-manifold with b1(M) = 1, and π1(M) has the same finite quotients as a free-by-cyclic grou...

The concept of logical fiberings is briefly summarized. Based on experiences with concrete examples an algorithmic approach is developed which leads to a represention of a many-valued logic as a logical fibering. The Stone isomorphism for expressing classical logical operations by corresponding polynomials can be extended to m-valued logics. On the basis of this, a classical deduction problem c...

In this paper we show Whitney’s fibering conjecture in the real and complex, local analytic and global algebraic cases. For a given germ of complex or real analytic set, we show the existence of a stratification satisfying a strong (real arc-analytic with respect to all variables and analytic with respect to the parameter space) trivialization property along each stratum. We call such a trivial...

We define a new condition on relatively hyperbolic Dehn filling which allows us to control the behavior of quasiconvex subgroups need not be full. As an application, in combination with recent work Cooper and Futer, we provide proof virtual fibering non-compact finite-volume $3$-manifolds, result first proved by Wise. Additionally, explain how previous results multiplicity height can generalize...