Incompressibility and fibrations

Diagonal Fibrations Are Pointwise Fibrations

On the category of bisimplicial sets there are different Quillen closed model structures associated to various definitions of fibrations. In one of them, which is due to Bousfield and Kan and that consists of seeing a bisimplicial set as a simplicial object in the category of simplicial sets, fibrations are those bisimplicial set maps such that each of the induced simplicial set maps is a Kan f...

Recurrence and Incompressibility

Incompressibility and Global Inversion

Given a local diffeomorphism f : R → R, we consider certain incompressibility conditions on the parallelepiped Df(x) ([0, 1]) which imply that the pre-image of an affine subspace is non-empty and has trivial homotopy groups. These conditions are then used to establish criteria for f to be globally invertible, generalizing in all dimensions the previous results of Sabatini.

Large Alphabets and Incompressibility

We briefly survey some concepts related to empirical entropy — normal numbers, de Bruijn sequences and Markov processes — and investigate how well it approximates Kolmogorov complexity. Our results suggest lth-order empirical entropy stops being a reasonable complexity metric for almost all strings of length m over alphabets of size n about when nl surpasses m.

Incompressibility and Least-area Surfaces

We show that if F is a smooth, closed, orientable surface embedded in a closed, orientable 3-manifold M such that for each Riemannian metric g on M , F is isotopic to a least-area surface F (g), then F is incompressible.