Equivariant Differential Characters and Symplectic Reduction

@article{Lerman2008EquivariantDC,
  title={Equivariant Differential Characters and Symplectic Reduction},
  author={Eugene Lerman and Anton Malkin},
  journal={Communications in Mathematical Physics},
  year={2008},
  volume={289},
  pages={777-801}
}
  • E. LermanA. Malkin
  • Published 1 July 2008
  • Mathematics
  • Communications in Mathematical Physics
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References

SHOWING 1-10 OF 21 REFERENCES

Differential characters as stacks and prequantization

We generalize geometric prequantization of symplectic manifolds to differentiable stacks. Our approach is atlas-independent and provides a bijection between isomorphism classes of principal circle

Equivariant smooth Deligne cohomology

On the basis of Brylinski’s work, we introduce a notion of equ ivariant smooth Deligne cohomology group, which is a generalization of both ordinary smooth Deligne cohomology and ordinary equivariant

Symplectic groupoids and Poisson manifolds

On definit la notion de groupoide symplectique. On donne la variete de Poisson de ce groupoide symplectique. On presente une construction

Differential Characters on Orbifolds and String Connections I

In this paper we introduce the Cheeger-Simons cohomology of a global quotient orbifold. We prove that the Cheeger-Simons cohomology of the orbifold is isomorphic to its Beilinson-Deligne cohomology.

Curvature and Characteristic Classes

Differential forms and cohomology.- Multiplicativity. The simplicial de rham complex.- Connections in principal bundles.- The chern-weil homomorphism.- Topological bundles and classifying spaces.-

Supersymmetry and equivariant de Rham theory

Higher regulators and values of L-functions

In the work conjectures are formulated regarding the value of L-functions of motives and some computations are presented corroborating them.

Quadratic functions in geometry, topology, and M-theory

We describe an interpretation of the Kervaire invariant of a Riemannian manifold of dimension $4k+2$ in terms of a holomorphic line bundle on the abelian variety $H^{2k+1}(M)\otimes R/Z$. Our results