Fibrations, unique path lifting, and continuous monodromy

On bifurcation braid monodromy of elliptic fibrations

Abstract. We define a monodromy homomorphism for irreducible families of regular elliptic fibrations which takes values in the mapping class group of a punctured sphere. In the computation we consider only elliptic fibrations which contain no singular fibres of types other than I1 and I ∗ 0 . We compare the maximal groups, which can be the monodromy groups of algebraic, resp. differentiable fam...

Stratified Path Spaces and Fibrations

The main objects of study are the homotopically stratified metric spaces introduced by Quinn. Closed unions of strata are shown to be stratified forward tame. Stratified fibrations between spaces with stratifications are introduced. Paths which lie in a single stratum except possibly at their initial points form a space with a natural stratification, and the evaluation map from that space of pa...

Rationality of Moduli of Elliptic Fibrations with Fixed Monodromy

— We prove rationality results for moduli spaces of elliptic K3 surfaces and elliptic rational surfaces with fixed monodromy groups.

On the Unique-Lifting Property

We study the uniqueness of minimal liftings of cut generating functions obtained from maximal lattice-free polytopes. We prove a basic invariance property of unique minimal liftings for general maximal lattice-free polytopes. This generalizes a previous result by Basu, Cornuéjols and Köppe [3] for simplicial maximal lattice-free polytopes, thus completely settling this fundamental question abou...

Continuous Fibrations and Inverse Limits of Toposes