Related papers: Symplectic monodromy, quasi-homogeneous polynomial…
We formulate certain sufficient conditions for the symplectic monodromy of an isolated quasihomogeneous singularity to be of infinite order in the relative symplectic mapping class group of the Milnor fibre and give a proof using Maslov…
The integral monodromy on the Milnor lattice of an isolated quasihomogeneous singularity is subject of an almost untouched conjecture of Orlik from 1972. We prove this conjecture for all iterated Thom-Sebastiani sums of chain type…
We calculate the eta-invariant for the odd signature operator relative to a specific submersion metric on the Milnor fibration of a quasihomogeneous hypersurface singularity using certain global boundary conditions in terms of the data of…
We compute the symplectic cohomology of Milnor fibers of isolated quasihomogeneous cAn singularities . In addition, we use our computations to distinguish their links as contact manifolds and to provide further evidence to a conjecture of…
The motivation for this paper are computer calculations of complete lists of weight systems of quasihomogeneous polynomials with isolated singularity at 0 up to rather large Milnor numbers. We review combinatorial characterizations of such…
We consider a continuous path of bounded symmetric Fredholm bilinear forms with arbitrary endpoints on a real Hilbert space, and we prove a formula that gives the spectral flow of the path in terms of the spectral flow of the restriction to…
We use topological methods to study various semicontinuity properties of spectra of singular points of plane algebraic curves and of polynomials in two variables at infinity. Using Seifert forms and the Tristram--Levine signatures of links,…
This paper studies how symplectic invariants created from Hamiltonian Floer theory change under the perturbations of symplectic structures, not necessarily in the same cohomology class. These symplectic invariants include spectral…
The spectral flow is a well-known quantity in spectral theory that measures the variation of spectra about $0$ along paths of selfadjoint Fredholm operators. The aim of this work is twofold. Firstly, we consider homotopy invariance…
Given a closed connected symplectic manifold $(M,\omega)$, we construct an alternating $\mathbb{R}$-bilinear form $\mathfrak{b}=\mathfrak{b}_{\mu_{\mathrm{Sh}}}$ on the real first cohomology of $M$ from Shelukhin's quasimorphism…
We consider homoclinic solutions for Hamiltonian systems in symplectic Hilbert spaces and generalise spectral flow formulas that were proved by Pejsachowicz and the author in finite dimensions some years ago. Roughly speaking, our main…
We build a combinatorial invariant, called the spectral monodromy from the spectrum of a non-selfadjoint h -pseudodifferential operator with two degrees of freedom in the semi-classical limit. We treat small non-selfadjoint perturbation of…
Let f be a hypersurface surface local singularity whose zero set has 1-dimensional singular locus. We develop an explicit procedure that provides the boundary of the Milnor fibre of f as an oriented plumbed 3-manifold. The method provides…
We use the notion of generalized signatures at a singularity of a smooth curve of symmetric bilinear forms to determine a formula for the computation of the Maslov index in the case of a real-analytic path having possibly non transversal…
Motivated by the earlier results, we study theoretically and numerically the asymptotics and the monodromy of the quasi-exactly solvable part of the spectrum of the quasi-exactly solvable quartic introduced by C.~M.~Bender and S.~Boettcher.…
The variation operator in singularity theory maps relative homology cycles to compact cycles in the Milnor fiber using the monodromy. We construct its symplectic analogue for an isolated singularity. We define the monodromy Lagrangian Floer…
We consider smooth flows preserving a smooth invariant measure, or, equivalently, locally Hamiltonian flows on compact orientable surfaces and show that almost every such locally Hamiltonian flow with only simple saddles has singular…
We give a topological model for a polynomial map from $\C^n$ to $\C$ in the neighborhood of a fiber with isolated singularities. This is motivated out of the ``unfolding of links'' described earlier by the first author and Lee Rudolph. The…
We study the monodromy diffeomorphism of Milnor fibrations of isolated complex surface singularities, by computing the family Seiberg--Witten invariant of Seifert-fibered Dehn twists using recent advances in monopole Floer homology. More…
The Mellin transform of fibre integral is calculated for certain isolated singularities of quasihomogeneous complete intersections (especially the unimodal singualrities of the list by Giusti and Wall). We show the property of symmetry…