Related papers: A relative Seidel morphism and the Albers map

Let ${\cal O}$ be a quantizable coadjoint orbit of a semisimple Lie group $G$. Under certain hypotheses we prove that $#(\pi_1(\text{Ham}({\cal O})))\geq #(Z(G))$, where $\text{Ham}({\cal O})$ is the group of Hamiltonian symplectomorphisms…

In this paper, we study the theory of non-abelian extensions of a Leibniz conformal algebra $R$ by a Leibniz conformal algebra $H$ and prove that all the non-abelian extensions are classified by non-abelian $2$nd cohomology $H^2_{nab}(R,H)$…

The adjacency matrix of a symplectic dual polar graph restricted to the eigenspaces of an abelian automorphism subgroup is shown to act as the adjacency matrix of a weighted subspace lattice. The connection between the latter and…

We introduce here a natural functional associated to any $b \in QH_* (M, \omega)$: \emph{spectral length functional}, on the space of "generalized paths" in $ \text {Ham}(M, \omega)$, closely related to both the Hofer length functional and…

To every closed subset $X$ of a symplectic manifold $(M,\omega)$ we associate a natural group of Hamiltonian diffeomorphisms $Ham(X,\omega)$. We equip this group with a semi-norm $\Vert\cdot\Vert^{X,\omega}$, generalizing the Hofer norm. We…

We are dealing with the complexity of the homeomorphism equivalence relation on some classes of metrizable compacta from the viewpoint of invariant descriptive set theory. We prove that the homeomorphism equivalence relation of absolute…

In this article the framework created by Cartan to produce local differential invariants for submanifolds of homogeneous spaces is applied to classify all totally geodesic Lagrangian submanifolds and all homogeneous Lagrangian submanifolds…

We extend the Cohen-Jones-Segal construction of stable homotopy types associated to flow categories of Morse-Smale functions $f$ to the setting where $f$ is equivariant under a finite group action and is Morse but no longer Morse-Smale.…

In this paper, first we give the notion of a crossed homomorphism on a 3-Lie algebra with respect to an action on another 3-Lie algebra, and characterize it using a homomorphism from a Lie algebra to the semidirect product Lie algebra. We…

We describe a procedure to attach a nilpotent strong homotopy Lie algebra to every simple hypergraph and prove that two hypergraphs are isomorphic if and only if the corresponding strong homotopy Lie algebras are isomorphic. As an…

We use results of Auroux arXiv:1001.4323 and Zemke arXiv:1801.09270 to prove that, in the morphism spaces formulation of Heegaard Floer homology given in arXiv:1005.1248, the opposite composition map agrees up to homotopy with the map on…

We consider symplectic Floer homology in the lowest nontrivial dimension, that is to say, for area-preserving diffeomorphisms of surfaces. Particular attention is paid to the quantum cap product; we show that it distinguishes the trivial…

Two natural symplectic constructions, the Lagrangian suspension and Seidel's quantum representation of the fundamental group of the group of Hamiltonian diffeomorphisms, Ham(M), with (M,\omega) a monotone symplectic manifold, admit…

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…

We construct a family of Lagrangian submanifolds in the Landau--Ginzburg mirror to the projective plane equipped with a binodal cubic curve as anticanonical divisor. These objects correspond under mirror symmetry to the powers of the…

We construct an embedding $\Phi$ of $[0,1]^{\infty}$ into $Ham(M, \omega)$, the group of Hamiltonian diffeomorphisms of a suitable closed symplectic manifold $(M, \omega)$. We then prove that $\Phi$ is in fact a quasi-isometry. After…

In the usual setup, the grading on Floer homology is relative: it is unique only up to adding a constant. "Graded Lagrangian submanifolds" are Lagrangian submanifolds with a bit of extra structure, which fixes the ambiguity in the grading.…

Consider a Maslov zero Lagrangian submanifold diffeomorphic to a Lie group on which an anti-symplectic involution acts by the inverse map of the group. We show that the Fukaya $A_\infty$ endomorphism algebra of such a Lagrangian is…

The Maurer-Cartan algebra of a Lagrangian $L$ is the algebra that encodes the deformation of the Floer complex $CF(L,L;\Lambda)$ as an $A_\infty$-algebra. We identify the Maurer-Cartan algebra with the $0$-th cohomology of the Koszul dual…

In this note, we examine the bundle picture of the pullback construction of Lie algebroids. The notion of submersions by Lie algebroids is introduced, which leads to a new proof of the local normal form for lie algebroid transversals of…