Generalized Complex Hamiltonian Torus Actions: Examples and Constraints

نویسندگان

  • THOMAS BAIRD
  • YI LIN
چکیده

Consider an effective Hamiltonian torus action T ×M → M on a topologically twisted, generalized complex manifold M of dimension 2n. We prove that the rank(T ) ≤ n − 2 and that the topological twisting survives Hamiltonian reduction. We then construct a large new class of such actions satisfying rank(T ) = n − 2, using a surgery procedure on toric manifolds.

برای دانلود رایگان 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

Generalized Geometry, Equivariant ∂∂-lemma, and Torus Actions

In this paper we first consider the Hamiltonian action of a compact connected Lie group on anH-twisted generalized complexmanifold M. Given such an action, we define generalized equivariant cohomology and generalized equivariant Dolbeault cohomology. If the generalized complex manifoldM satisfies the ∂∂-lemma, we prove that they are both canonically isomorphic to (Sg)⊗HH(M), where (Sg ) is the ...

متن کامل

∂∂-lemma, and Torus Actions

In this paper we first consider the Hamiltonian action of a compact connected Lie group on anH-twisted generalized complexmanifold M. Given such an action, we define generalized equivariant cohomology and generalized equivariant Dolbeault cohomology. If the generalized complex manifoldM satisfies the ∂̄∂-lemma, we prove that they are both canonically isomorphic to (Sg)⊗HH(M), where (Sg ) is the ...

متن کامل

On the Existence of Star Products on Quotient Spaces of Linear Hamiltonian Torus Actions Hans-christian Herbig, Srikanth B. Iyengar and Markus J. Pflaum

We discuss BFV deformation quantization [5] in the special case of a linear Hamiltonian torus action. In particular, we show that the Koszul complex on the moment map of an effective linear Hamiltonian torus action is acyclic. We rephrase the nonpositivity condition of [2] for linear Hamiltonian torus actions. It follows that reduced spaces of such actions admit continuous star products.

متن کامل

The Equivariant Cohomology Theory of Twisted Generalized Complex Manifolds

It has been shown recently by Kapustin and Tomasiello that the mathematical notion of Hamiltonian actions on twisted generalized Kähler manifolds is in perfect agreement with the physical notion of general (2, 2) gauged sigma models with three-form fluxes. In this article, we study the twisted equivariant cohomology theory of Hamiltonian actions on H-twisted generalized complex manifolds. If th...

متن کامل

On the Existence of Star Products on Quotient Spaces of Linear Hamiltonian Torus Actions

We discuss BFV deformation quantization (Bordemann et al. in A homological approach to singular reduction in deformation quantization, singularity theory, pp. 443– 461. World Scientific, Hackensack, 2007) in the special case of a linear Hamiltonian torus action. In particular, we show that the Koszul complex on the moment map of an effective linear Hamiltonian torus action is acyclic. We rephra...

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

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2009