We show that free-by-free groups satisfying a homological criterion, which we call excessive homology, are incoherent. This class is large in nature, including many examples of hyperbolic and non-hyperbolic groups. apply this criterion to finite index subgroups F 2 ?F n incoherence all such groups, other similar classes Furthermore, free-by-free, surface-by-surface, finitely generated-by-RAAG, ...

It is know that the Alexander polynomial detects fibered knots and 3-manifolds that fiber over the circle. In this note, we show that when the Alexander polynomial becomes inconclusive, the notion of “knot adjacency”, studied in [KL], can be used to obtain obstructions to fibering of knots and of 3-manifolds. As an application, given a fibered knot K′, we construct infinitely many non-fibered k...

Recall that the rank of a finitely generated group is the minimal number of elements needed to generate it. In [Whi02], M. White proved that the injectivity radius of a closed hyperbolic 3-manifold M is bounded above by some function of rank(π1(M)). Building on a technique that he introduced, we determine the ranks of the fundamental groups of a large class of hyperbolic 3-manifolds fibering ov...

Our main result is a generalization of Cappell’s 5-dimensional splitting theorem. As an application, we analyze, up to internal s-cobordism, the smoothable splitting and fibering problems for certain 5-manifolds mapping to the circle. For example, these maps may have homotopy fibers which are in the class of finite connected sums of certain geometric 4-manifolds. Most of these homotopy fibers h...

Exact squares in Cat are not necessarily absolute (i.e. preserved by any 2-functor Cat→ Cat), or even preserved by any 2-functor given by exponentiation (−)I : Cat → Cat: if a square is preserved by exponentiation it will be called a contractible exact square. We will characterize diagrammatically these contractible squares, and among them the contractible categories, and the so called fibering...

We describe a class of (2,2) superconformal field theories obtained by fibering a Landau-Ginzburg orbifold CFT over a compact Kähler base manifold. While such models are naturally obtained as phases in a gauged linear sigma model, our construction is independent of such an embedding. We discuss the general properties of such theories and present a technique to study the massless spectrum of the...

We consider a family of polyharmonic problems of the form (−∆)mu = g(x,u) in Ω, Dαu = 0 on ∂Ω, where Ω ⊂ Rn is a bounded domain, g(x,·) ∈ L∞(Ω), and |α| < m. By using the fibering method, we obtain some results about the existence of solution and its multiplicity under certain assumptions on g. We also consider a family of biharmonic problems of the form ∆2u+ (∆φ+ |∇φ|2)∆u+ 2∇φ ·∇∆u = g(x,u), w...