相关论文: Lagrangian concordance is not a partial order in h…

It is shown that the N-Galilean conformal algebra, with N-odd, is the maximal symmetry algebra of the free Lagrangian involving (N+1)/2-th order time derivative.

In this paper, we consider exact Lagrangian cobordisms and the map they induce on the Chekanov-Eliashberg DGAs of their Legendrian ends as defined by Ekholm, Honda, and Kalman. Specifically, we show how to adapt this map to linearizations…

Let $M$ be a closed manifold. We introduce a family of Legendrian isotopy invariants for Legendrians in $J^1M$, which we collectively call Legendrian higher torsion. Given a choice of a class $\mathcal{F}$ of fibre bundles over $M$,…

We show that there exists a Legendrian knot with maximal Thurston-Bennequin invariant whose contact homology is trivial. We also provide another Legendrian knot which has the same knot type and classical invariants but nonvanishing contact…

In our previous article Phys. Rev. Lett. 127 (2021) 271601, we announced a novel 'democratic' Lagrangian formulation of general nonlinear electrodynamics in four dimensions that features electric and magnetic potentials on equal footing.…

Under certain assumptions (such as weak exacteness or monotonicity) we show that splitting Lagrangians through cobordism has an energy cost and, from this cost being smaller than certain explicit bounds, we deduce some strong forms of…

We present three Lagrangian algebras in the modular 2-category associated to the 3+1D $\mathbb{Z}_2$ topological order and discuss their physical interpretations, connecting algebras with gapped boundary conditions, and interestingly, maps…

Given a symplectic manifold M, we consider a category with objects finite ordered families of Lagrangian submanifolds of M (subject to certain additional constraints) and with morphisms Lagrangian cobordisms relating them. We construct a…

We characterize which Legendrian $4$-plat knots in the standard contact $3$-space have exact orientable Lagrangian fillings. As a corollary, we show that the underlying smooth knot types of fillable Legendrian $4$-plats are positive.

For a certain class of exotic contact manifolds of dimension greater than 3, we show that there is an abundance of closed exact Lagrangians in their symplectization. All of these Lagrangians are displaceable by Hamiltonian isotopy, and many…

For an exact Lagrangian cobordism $L$ between Legendrians in $J^1(M)$ from $\Lambda_-$ to $\Lambda_+$ whose Legendrian lift is $\widetilde{L}$, we prove that sheaves in $Sh_{\widetilde{L}}(M \times \mathbb{R} \times \mathbb{R}_{>0})$ are…

We extend the definition of Lagrangian quantum homology to monotone Lagrangian cobordism and establish its general algebraic properties. In particular we develop a relative version of Lagrangian quantum homology associated to a cobordism…

We prove that Legendrian and transverse links in overtwisted contact structures having overtwisted complements can be classified coarsely by their classical invariants. We further prove that any coarse equivalence class of loose links has…

Take a sequence of contactomorphisms of a contact three-manifold that $C^0$-converges to a homeomorphism. If the images of a Legendrian knot limit to a smooth knot under this sequence, we show that it is Legendrian. We prove this by…

We study correlation functions in five-dimensional non-Lorentzian theories with an $SU(1,3)$ conformal symmetry. Examples of such theories have recently been obtained as $\Omega$-deformed Yang-Mills Lagrangians arising from a null reduction…

We prove that there are at least seeds many exact embedded Lagrangian fillings for Legendrian links of type $\mathsf{ADE}$. We also provide seeds many Lagrangian fillings with certain symmetries for type $\mathsf{BCFG}$. Our main tools are…

We discuss a correspondence between certain contact pairs on the one hand, and certain locally conformally symplectic forms on the other. In particular, we characterize these structures through suspensions of contactomorphisms. If the…

We construct infinite families of non-simple isotopy classes of links in overtwisted contact structures on $S^1$-bundles over surfaces. These examples include: (1) a pair of Legendrian links that are not Legendrian isotopic, but which are…

Complete integrability in a symplectic setting means the existence of a Lagrangian foliation leaf-wise preserved by the dynamics. In the paper we describe complete integrability in a contact set-up as a more subtle structure: a flag of two…

We find new obstructions on the topology of monotone Lagrangian submanifolds of $C^{n}$ under some hypothesis on the homology of their universal cover. In particular we show that nontrivial connected sums of manifolds of odd dimensions do…