Each Lie algebra of vector fields (e.g. those which are tangent to a foliation) of a smooth manifold définies, in a natural way, a spectral sequence which converges to the de Rham cohomology of in a finite number of steps. We prove e.g. that for all there exists a foliated compact manifold with infinite dimensional.
A conjecture of [swTAMS] states that a knot is nonfibered if and only if its infinite cyclic cover has uncountably many finite covers. We prove the conjecture for a class of knots that includes all knots of genus 1, using techniques from symbolic dynamics.
We discuss some properties of an orthogonal projection onto a subset of a Euclidean space. The special stress is laid on projection's regularity and characterization of the interior of its domain.
We show that the subgroup of the knot concordance group generated by links of isolated complex singularities intersects the subgroup of algebraically slice knots in an infinite rank subgroup.