Related papers: Spectral selectors and contact orderability

We construct a spectral sequence converging to the cohomology with compact support of the m-th contact locus of a complex polynomial. The first page is explicitly described in terms of a log resolution and coincides with the first page of…

In this note, we observe that the hat version of the Heegaard Floer invariant of Legendrian knots in contact three-manifolds defined by Lisca-Ozsvath-Stipsicz-Szabo can be combinatorially computed. We rely on Plamenevskaya's combinatorial…

We study collections of exact Lagrangian submanifolds respecting some uniform Riemannian bounds, which we equip with a metric naturally arising in symplectic topology (e.g. the Lagrangian Hofer metric or the spectral metric). We exhibit…

In this paper, we prove that there exists a residual subset of contact forms $\lambda$ (if any) on a compact connected orientable manifold $M$ for which the foliation de Rham cohomology of the associated Reeb foliation $F_\lambda$ is…

Chordal clutters in the sense of [14] and [3] are defined via simplicial orders. Their circuit ideal has a linear resolution, independent of the characteristic of the base field. We show that any Betti sequence of an ideal with linear…

We construct a combinatorial invariant of Legendrian knots in standard contact three-space. This invariant, which encodes rational relative Symplectic Field Theory and extends contact homology, counts holomorphic disks with an arbitrary…

We classify all closed, aspherical Riemannian manifolds M whose universal cover has indiscrete isometry group. One sample application is the theorem that any such M with word-hyperbolic fundamental group must be isometric to a negatively…

We establish a general link between integrable systems in algebraic geometry (expressed as Jacobian flows on spectral curves) and soliton equations (expressed as evolution equations on flat connections). Our main result is a natural…

In this short note we provide the examples of pairs of closed, connected Legendrian non-isotopic Legendrian submanifolds $(\Lambda_{-}, \Lambda_{+})$ of the $(4n+1)$-dimensional contact vector space, $n>1$, such that there exist Lagrangian…

We relate non-orderability in contact topology to shortening in the contact Hofer norm. Combined with considerations of open books, this provides many new examples of non-orderable contact manifolds, including contact boundaries of…

For a compact set $K$ with contact type boundary in a symplectic manifold $M$ we construct a spectral sequence from the local Floer homology of the Reeb orbits, as studied by \cite{Mclean2012}, to the relative symplectic cohomology of $K$…

Gromov's famous non-squeezing theorem (1985) states that the standard symplectic ball cannot be symplectically squeezed into any cylinder of smaller radius. Does there exist an analogue of this result in contact geometry? Our main finding…

We discuss the Mayer-Vietoris spectral sequence as an invariant in the context of persistent homology. In particular, we introduce the notion of $\varepsilon$-acyclic carriers and $\varepsilon$-acyclic equivalences between filtered regular…

We define a new family of spectral invariants associated to certain Lagrangian links in compact and connected surfaces of any genus. We show that our invariants recover the Calabi invariant of Hamiltonians in their limit. As applications,…

We show that positive $S^1$-equivariant symplectic homology is a contact invariant for a subclass of contact manifolds which are boundaries of Liouville domains. In nice cases, when the set of Conley-Zehnder indices of all good periodic…

The singular real second order 1D Schrodinger operators are considered here with such potentials that all local solutions near singularities to the eigenvalue problem are meromorphic for all values of the spectral parameter. All…

Seidel-Smith and Hendricks used equivariant Floer cohomology to define some spectral sequences from symplectic Khovanov homology and Heegaard Floer homology. These spectral sequences give rise to Smith-type inequalities. Similar-looking…

Localization of Floer homology is first introduced by Floer \cite{floer:fixed} in the context of Hamiltonian Floer homology. The author employed the notion in the Lagrangian context for the pair $(\phi_H^1(L),L)$ of compact Lagrangian…

We study continuous selections of the set-valued map that takes every skew-symmetric bilinear form on a vector space to its corresponding set of maximal isotropic subspaces. Applications are made to establishing continuity properties of the…

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…