We introduce the notion of fractional bidromy which is the combination of fractional monodromy and bidromy, two recent generalizations of Hamiltonian monodromy. We consider the vibrational spectrum of the HOCl molecule which is used as an illustrative example to show the presence of nontrivial fractional bidromy. To our knowledge, this is the first example of a molecular system where such a gen...

We clarify the algebraic structure of continuous and discrete quasi-exactly solvable spectral problems by embedding them into the framework of the quantum inverse scattering method. The quasi-exactly solvable hamiltonians in one dimension are identified with traces of quantum monodromy matrices for specific integrable systems with non-periodic boundary conditions. Applications to the Azbel-Hofs...

We compute the Poisson bracket relations for the monodromy matrix of the auxiliary linear problem. If the basic Poisson brackets of the model contain derivatives, this computation leads to a peculiar kind of symmetry breaking which accounts for a 'spontaneous quantiza-tion' of the underlying global gauge group. A classification of possible patterns of symmetry breaking is outlined.

In this paper we give a very easy to compute necessary condition in the monodromy problem for all singular point of analytic differential systems in the real plane. Our main tool is considering the analytic function, angular speed, and studying its limit through straight lines to the singular point. 2000 AMS Subject Classification: 34C05, 34C20, 34C35, 58F21

Given a complex analytic function with a one-dimensional critical locus at the origin, we examine the monodromy action on the integral cohomology of the Milnor fiber. We relate this monodromy to that of a generic hyperplane slice through the origin, and to that of a generic hyperplane slice near the origin. We thereby obtain number-theoretic restrictions on the monodromy and on the cohomology o...

We study a problem related to Kontsevich’s homological mirror symmetry conjecture for the case of a generic curve Y with bi-degree (2,2) in a product of projective lines P×P. We calculate two differenent monodromy representations of period integrals for the affine variety X obtained by the dual polyhedron mirror variety construction from Y. The first method that gives a full representation of t...

In this paper we study the monodromy groups of projections of smooth irreducible surfaces in P3 from points. Our particular interest lies in finding whether the monodromy group of a projection πL of a surface from a point L is the whole symmetric group or not. In the former case, we call L uniform, and in the latter case, not uniform. The very same terminology is also used for the whole project...

The aim of this paper is to use mapping class group relations to approach the ‘geography’ problem for Stein fillings of a contact 3-manifold. In particular, we adapt a formula of Endo and Nagami so as to calculate the signature of such fillings as a sum of the signatures of basic relations in the monodromy of a related open book decomposition. We combine this with a theorem of Wendl to show tha...