相关论文: Stability conditions in symplectic topology

This paper contains an overview of background from stable homotopy theory used by Freed--Hopkins in their work on invertible extended topological field theories. We provide a working guide to the stable homotopy category, to the Steenrod…

Let $X$ be a smooth compact complex surface with the canonical divisor $K_X$ ample and let $\Theta_X$ be its holomorphic tangent bundle. Bridgeland stability conditions are used to study the space $H^1 (\Theta_X)$ of infinitesimal…

We describe the relationship between two spaces associated to a quiver with potential. The first is a complex manifold parametrizing Bridgeland stability conditions on a triangulated category, and the second is a cluster variety with a…

We provide a new proof of Ishii's conjecture for any dihedral reflection group $G\subset GL_2(\mathbb{C})$ from the viewpoint of Bridgeland stability conditions. Our strategy is to reduce the problem, via the derived McKay correspondence,…

We show the existence of Gepner type Bridgeland stability conditions on the triangulated categories of graded matrix factorizations associated with homogeneous polynomials which define general cubic fourfolds containing a plane. The key…

We adapt algorithms for resolving the singularities of complex algebraic varieties to prove that the natural map of homology theories from complex bordism to the bordism theory of complex derived orbifolds splits. In equivariant stable…

We study conditions on the topological D-branes of types A and B obtained by requiring a proper matching of the spectral flow operators on the boundary. These conditions ensure space-time supersymmetry and stability of D-branes. In most…

Under non-equilibrium conditions, bosonic modes can become dynamically unstable with an exponentially growing occupation. On the other hand, topological band structures give rise to symmetry protected midgap states. In this letter, we…

On a triangulated category $\mathbf D$ equipped with a semiorthogonal decomposition $\mathbf D=\langle{\mathbf D_{1}},{\mathbf D_{2}}\rangle$, Collins and Polishchuk develop a gluing construction of stability condition on $\mathbf D$. The…

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…

We present the Hamiltonian formalism for the Euler equation of symplectic fluids, introduce symplectic vorticity, and study related invariants. In particular, this allows one to extend D.Ebin's long-time existence result for geodesics on…

We study deformations of symplectic structures on a smooth manifold $M$ via the quasi-Poisson theory. By a fact, we can deform a given symplectic structure $\omega $ to a new symplectic structure $\omega_t$ parametrized by some element $t$…

We prove that some of the classical homological stability results for configuration spaces of points in manifolds can be lifted to motivic cohomology.

We explain how structures analogous to those appearing in the theory of stability conditions on abelian and triangulated categories arise in geometric invariant theory. This leads to an axiomatic notion of a central charge on a scheme with…

Asymptotic behaviour of a tippe top, under the action of gliding friction. Liapunov stability analysis of the asymptotics of states with arbitrary initial conditions.

We consider the stability of synchronized states (including equilibrium point, periodic orbit or chaotic attractor) in arbitrarily coupled dynamical systems (maps or ordinary differential equations). We develop a general approach, based on…

We obtain sufficient conditions for the stability of the synchronized solutions for a class of coupled dynamical systems. This is accomplished by finding an analytical expression for the transverse Liapunov exponent through spectral…

A synergetic model describing the state of an ultrathin lubricant layer squeezed between two atomically smooth solid surfaces operating in the boundary friction mode has been developed further. To explain the presence of different operation…

A method for testing $G_\mu$-stability of relative equilibria in Hamiltonian systems of the form "kinetic + potential energy" is presented. This method extends the Reduced Energy-Momentum Method of Simo et al. to the case of non-free group…

We obtain a rigidity result of symplectic translating solitons via the complex phase map. It indicates that we can remove the bounded second fundamental form assumption for symplectic translating solitons in [13].