compact symplectic manifold
Recently Published Documents


TOTAL DOCUMENTS

9
(FIVE YEARS 0)

H-INDEX

3
(FIVE YEARS 0)

2020 ◽  
Vol 13 (4) ◽  
pp. 89-115
Author(s):  
Kaoru Ono ◽  
Hong Van Le

This note is mostly an exposition of a few versions of Floer-Novikov cohomology with a few new observations. For example, we state a lower bound for the number of symplectic fixed points of a non-degenerate symplectomorphism, which is symplectomorphic isotopic to the identity, on a compact symplectic manifold, more precisely than previous statements in [14,10].


Author(s):  
Fumihiko Sanda

Abstract Assume the existence of a Fukaya category $\textrm{Fuk}(X)$ of a compact symplectic manifold $X$ with some expected properties. In this paper, we show $\mathscr{A} \subset \textrm{Fuk}(X)$ split generates a summand $\textrm{Fuk}(X)_e \subset \textrm{Fuk}(X)$ corresponding to an idempotent $e \in QH^{\bullet }(X)$ if the Mukai pairing of $\mathscr{A}$ is perfect. Moreover, we show $HH^{\bullet }(\mathscr{A}) \cong QH^{\bullet }(X) e$. As an application, we compute the quantum cohomology and the Fukaya category of a blow-up of $\mathbb{C} P^2$ at four points with a monotone symplectic structure.


2016 ◽  
Vol 13 (02) ◽  
pp. 1650007
Author(s):  
Nikolai Tarkhanov

We describe a natural construction of deformation quantization on a compact symplectic manifold with boundary. On the algebra of quantum observables a trace functional is defined which as usual annihilates the commutators. This gives rise to an index as the trace of the unity element. We formulate the index theorem as a conjecture and examine it by the classical harmonic oscillator.


2015 ◽  
Vol 12 (03) ◽  
pp. 1550030
Author(s):  
Indranil Biswas ◽  
Saikat Chatterjee ◽  
Rukmini Dey

Given a compact symplectic manifold M, with integral symplectic form, we prequantize a certain class of functions on the path space for M. The functions in question are induced by functions on M. We apply our construction to study the symplectic structure on the solution space of Klein–Gordon equation.


2015 ◽  
Vol 12 (02) ◽  
pp. 1550021
Author(s):  
Dong Zhang ◽  
Bohui Chen ◽  
Cheng-Yong Du

In this paper, we give a quantum modification of the relative cup product on H*(X, S;ℝ) by using Gromov–Witten invariants when S is a compact codimension 2k symplectic submanifold of the compact symplectic manifold (X, ω).


2012 ◽  
Vol 23 (10) ◽  
pp. 1250102 ◽  
Author(s):  
ROBERTO PAOLETTI

In recent years, the near diagonal asymptotics of the equivariant components of the Szegö kernel of a positive line bundle on a compact symplectic manifold have been studied extensively by many authors. As a natural generalization of this theme, here we consider the local scaling asymptotics of the Toeplitz quantization of a Hamiltonian symplectomorphism, and specifically how they concentrate on the graph of the underlying classical map.


2010 ◽  
Vol 31 (4) ◽  
pp. 1237-1247 ◽  
Author(s):  
ALVARO PELAYO ◽  
SUSAN TOLMAN

AbstractThe study of fixed points is a classical subject in geometry and dynamics. If the circle acts in a Hamiltonian fashion on a compact symplectic manifold M, then it is classically known that there are at least $\frac {1}{2}\,{\dim M}+1$ fixed points; this follows from Morse theory for the momentum map of the action. In this paper we use Atiyah–Bott–Berline–Vergne (ABBV) localization in equivariant cohomology to prove that this conclusion also holds for symplectic circle actions with non-empty fixed sets, as long as the Chern class map is somewhere injective—the Chern class map assigns to a fixed point the sum of the action weights at the point. We complement this result with less sharp lower bounds on the number of fixed points, under no assumptions; from a dynamical systems viewpoint, our results imply that there is no symplectic periodic flow with exactly one or two equilibrium points on a compact manifold of dimension at least eight.


2009 ◽  
Vol 11 (06) ◽  
pp. 895-936 ◽  
Author(s):  
HAI-LONG HER

Let (M,ω) be a compact symplectic manifold, and ϕ be a symplectic diffeomorphism on M, we define a Floer-type homology FH*(ϕ) which is a generalization of Floer homology for symplectic fixed points defined by Dostoglou and Salamon for monotone symplectic manifolds. These homology groups are modules over a suitable Novikov ring and depend only on ϕ up to a Hamiltonian isotopy.


Sign in / Sign up

Export Citation Format

Share Document