Example of a Non-log-concave Duistermaat-heckman Measure
نویسنده
چکیده
We construct a compact symplectic manifold with a Hamiltonian circle action for which the Duistermaat-Heckman function is not log-concave.
منابع مشابه
The Log-concavity Conjecture for the Duistermaat-heckman Measure Revisited
Karshon constructed the first counterexample to the log-concavity conjecture for the Duistermaat-Heckman measure: a Hamiltonian six manifold whose fixed points set is the disjoint union of two copies of T. In this article, for any closed symplectic four manifold N with b > 1, we show that there is a Hamiltonian circle manifold M fibred over N such that its DuistermaatHeckman function is not log...
متن کاملLog-Concavity and Symplectic Flows
We prove the logarithmic concavity of the Duistermaat-Heckman measure of an Hamiltonian (n− 2)-dimensional torus action for which there exists an effective commuting symplectic action of a 2-torus with symplectic orbits. Using this, we show that any symplectic (n− 2)-torus action with non-empty fixed point set which satisfies this additional 2-torus condition must be Hamiltonian.
متن کاملDuistermaat-Heckman Theorem
Lutian Zhao UID: 661622198 The Duistermaat-Heckman theorems concern the measure associated to moment map of a torus action of symplectic manifold. Typically, this name refers to two theorems, one is called the ”Duistermaat-Heckman measure", which says that ”the Radon-Nikodym derivative is piecewise polynomial", the definition of each terms will be introduced later. The second one is called ”Dui...
متن کاملDuistermaat-Heckman measures in a non-compact setting
We prove a Duistermaat-Heckman type formula in a suitable non-compact setting. We use this formula to evaluate explicitly the pushforward of the Liouville measure via the moment map of both an abelian and a non-abelian group action. As an application we obtain the classical analogues of well-known multiplicity formulas for the holomorphic discrete series representations.
متن کاملConformal Motions and the Duistermaat-Heckman Integration Formula
We derive a geometric integration formula for the partition function of a classical dynamical system and use it to show that corrections to the WKB approximation vanish for any Hamiltonian which generates conformal motions of some Riemannian geometry on the phase space. This generalizes previous cases where the Hamiltonian was taken as an isometry generator. We show that this conformal symmetry...
متن کامل