Related papers: Function theoretical applications of Lagrangian sp…
Starting from a Heegaard splitting of a three-manifold, we use Lagrangian Floer homology to construct a three-manifold invariant, in the form of a relatively Z/8-graded abelian group. Our motivation is to have a well-defined symplectic side…
Using quilted Floer cohomology and relative quilt invariants, we define a composition functor for categories of Lagrangian correspondences in monotone and exact symplectic Floer theory. We show that this functor agrees with geometric…
This is the first of two articles aiming to introduce symplectic spinors into the field of symplectic topology and the subject of Frobenius structures. After exhibiting a (tentative) axiomating setting for Frobenius structures resp. 'Higgs…
A new relation between homoclinic points and Lagrangian Floer homology is presented: In dimension two, we construct a Floer homology generated by primary homoclinic points. We compute two examples and prove an invariance theorem. Moreover,…
This article gives a classification, up to symplectic equivalence, of singular Lagrangian foliations given by a completely integrable system of a 4-dimensional symplectic manifold, in a full neighbourhood of a singular leaf of focus-focus…
In this paper we define invariants of Hamiltonian group actions for central regular values of the moment map. The key hypotheses are that the moment map is proper and that the ambient manifold is symplectically aspherical. The invariants…
The central theme of this paper is the holomorphic spectral theory of the canonical Laplace operator of the complement $\Omega := \{(z,w) \in \widehat{\mathbb{C}}^2 \colon z \cdot w \neq 1\}$ of the "complexified unit circle" $\{(z,w) \in…
We construct a $GL$-invariant measure on a semi-infinite Grassmannian over a finite field, describe the natural group of symmetries of this measure, and decompose the space $L^2$ over the Grassmannian on irreducible representations. The…
Link Floer homology is an invariant for links defined using a suitable version of Lagrangian Floer homology. In an earlier paper, this invariant was given a combinatorial description with mod 2 coefficients. In the present paper, we give a…
For each positive integer n, Khovanov and Rozansky constructed an invariant of links in the form of a doubly-graded cohomology theory whose Euler characteristic is the sl(n) link polynomial. We use Lagrangian Floer cohomology on some…
We show that in many examples the non-displaceability of Lagrangian submanifolds by Hamiltonian isotopy can be proved via Lagrangian Floer cohomology with non-unitary line bundle. The examples include all monotone Lagrangian torus fibers in…
We provide the spectral expansion in a weighted Hilbert space of a substantial class of invariant non-self-adjoint and non-local Markov operators which appear in limit theorems for positive-valued Markov processes. We show that this class…
Given a symplectic cohomology class of degree 1, we define the notion of an equivariant Lagrangian submanifold. The Floer cohomology of equivariant Lagrangian submanifolds has a natural endomorphism, which induces a grading by generalized…
The Upsilon invariant of a knot is a concordance invariant derived from knot Floer homology theory. It is a piecewise linear continuous function defined on the interval $[0,2]$. Borodzik and Hedden gave a question asking for which knots the…
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…
In a previous article, we proved that symplectic homeomorphisms preserving a coisotropic submanifold C, preserve its characteristic foliation as well. As a consequence, such symplectic homeomorphisms descend to the reduction of the…
E. Noether's general analysis of conservation laws has to be completed in a Lagrangian theory with local gauge invariance. Bulk charges are replaced by fluxes of superpotentials. Gauge invariant bulk charges may subsist when distinguished…
We show that the conformally invariant fractional powers of the sub-Laplacian on the Heisenberg group are given in terms of the scattering operator for an extension problem to the Siegel upper halfspace. Remarkably, this extension problem…
We assign to each nondegenerate Hamiltonian on a closed symplectic manifold a Floer-theoretic quantity called its "boundary depth," and establish basic results about how the boundary depths of different Hamiltonians are related. As…
We establish an edge of the wedge theorem for the sheaf of holomorphic functions with exponential growth at infinity and construct the sheaf of Laplace hyperfunctions in several variables. We also study the fundamental properties of the…