Maximal Tori in Contactomorphism Groups

نویسنده

  • CHARLES P. BOYER
چکیده

I describe a general scheme which associates conjugacy classes of tori in the contactomorphism group to transverse almost complex structures on a compact contact manifold. Moreover, to tori of Reeb type whose Lie algebra contains a Reeb vector field one can associate a Sasaki cone. Thus, for contact structures D of K-contact type one obtains a configuration of Sasaki cones called a bouquet such that each Sasaki cone is associated with a conjugacy class of tori of Reeb type.

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Maximal Tori in the Contactomorphism Groups of Circle Bundles over Hirzebruch Surfaces

In a recent preprint Yael Karshon showed that there exist non-conjugate tori in a group of symplectomorphisms of a Hirzebruch surface. She counted them in terms of the cohomology class of the symplectic structure. We show that a similar phenomenon exists in the contactomorphism groups of pre-quantum circle bundles over Hirzebruch surfaces. Note that the contact structures in question are fillab...

متن کامل

On Maximal Tori in the Contactomorphism Groups of Regular Contact Manifolds

By a theorem of Banyaga the group of diffeomorphisms of a manifold P preserving a regular contact form α is a central S extension of the commutator of the group of symplectomorphisms of the base B = P/S. We show that if T is a Hamiltonian maximal torus in the group of symplectomorphism of B, then its preimage under the extension map is a maximal torus not only in the group Diff (P, α) of diffeo...

متن کامل

Normalizers of Maximal Tori

Normalizers and p-normalizers of maximal tori in p-compact groups can be characterized by the Euler characteristic of the associated homogeneous spaces. Applied to centralizers of elementary abelian p-groups these criteria show that the normalizer of a maximal torus of the centralizer is given by the centralizer of a preferred homomorphism to the normalizer of the maximal torus; i.e. that “norm...

متن کامل

Zero-groups and maximal tori

We give a presentation of various results on zero-groups in o-minimal structures together with some new observations. In particular we prove that if G is a definably connected definably compact group in an o-minimal expansion of a real closed field, then for any maximal definably connected abelian subgroup T of G, G is the union of the conjugates of T . This can be seen as a generalization of t...

متن کامل

Computing Maximal Tori Using LiE and Mathematica

This paper describes an algorithm for computing maximal tori of the reductive centralizer of a nilpotent element of an exceptional complex symmetric space. It illustrates also a good example of the use of Computer Algebra Systems to help answer important questions in the field of pure mathematics. Such tori play a fundamental rôle in several problems such as: classification of nilpotent orbits ...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2010