Given a projective surface and a generic projection to the plane, the braid monodromy factorization (and thus, the braid monodromy type) of the complement of its branch curve is one of the most important topological invariants ([10]), stable on deformations. From this factorization, one can compute the fundamental group of the complement of the branch curve, either in C or in CP. In this articl...

We determine parts of the contact homology of certain contact 3-manifolds in the framework of open book decompositions, due to Giroux. We study two cases: when the monodromy map of the compatible open book is periodic and when it is pseudo-Anosov. For an open book with periodic monodromy, we verify the Weinstein conjecture. In the case of an open book with pseudo-Anosov monodromy, suppose the b...

Following Newton, Ivory and Arnold, we study the Newtonian potentials of algebraic hypersurfaces in R. The ramification of (analytic continuations of) these potential depends on a monodromy group, which can be considered as a proper subgroup of the local monodromy group of a complete intersection (acting on a twisted vanishing homology group if n is odd). Studying this monodromy group we prove,...

This paper studies Heegaard splittings of surface bundles via the curve complex of the fibre. The translation distance of the monodromy is the smallest distance it moves any vertex of the curve complex. We prove that the translation distance is bounded above in terms of the genus of any strongly irreducible Heegaard splitting. As a consequence, if a splitting surface has small genus compared to...

We describe algorithmic methods for the Gauss-Manin connection of an isolated hypersurface singularity based on the microlocal structure of the Brieskorn lattice. They lead to algorithms for computing invariants like the monodromy, the spectrum, the spectral pairs, and M. Saito’s matrices A0 and A1. These algorithms use a normal form algorithm for the Brieskorn lattice, standard basis methods f...

Multisummation provides a transparent description of Stokes matrices which is reviewed here together with some applications. Examples of moduli spaces for Stokes matrices are computed and discussed. A moduli space for a third Painlevé equation is made explicit. It is shown that the monodromy identity, relating the topological monodromy and Stokes matrices, is useful for some quantum differentia...

Excluding a precise list of groups like alternating, symmetric, cyclic and dihedral, from 1st year algebra (§7.2.3), we expect there are only finitely many monodromy groups of primitive genus 0 covers. Denote this nearly proven genus 0 problem as Problem 2 . We call the exceptional groups 0-sporadic. Example: Finitely many Chevalley groups are 0-sporadic. A proven result: Among polynomial 0-spo...

We show that the hydrogen atom in orthogonal electric and magnetic fields has a special property of certain integrable classical Hamiltonian systems known as monodromy. The strength of the fields is assumed to be small enough to validate the use of a truncated normal form Hsnf which is obtained from a two step normalization of the original system. We consider the level sets of Hsnf on the secon...

The gauge action of the Lie groupG on the chiral WZNW phase spaceMǦ of quasiperiodic fields with Ǧ-valued monodromy, where Ǧ ⊂ G is an open submanifold, is known to be a Poisson-Lie (PL) action with respect to any coboundary PL structure on G, if the Poisson bracket on MǦ is defined by a suitable monodromy dependent exchange r-matrix. We describe the momentum map for these symmetries when G is ...