# Pontryagin forms on (4r−2)-manifolds and symplectic structures on the spaces of Riemannian metrics

@article{Prez2005PontryaginFO, title={Pontryagin forms on (4r−2)-manifolds and symplectic structures on the spaces of Riemannian metrics}, author={Roberto Ferreiro P{\'e}rez and Jaime Mu{\~n}oz Masqu{\'e}}, journal={Differential Geometry and Its Applications}, year={2005}, volume={30}, pages={206-215} }

## 10 Citations

Equivariant prequantization bundles on the space of connections and characteristic classes

- Mathematics
- 2017

We show how characteristic classes determine equivariant prequantization bundles over the space of connections on a principal bundle. These bundles are shown to generalize the Chern–Simons line…

Equivariant differential characters in Gauge Theory

- Mathematics
- 2019

Equivariant differential characters of second order are defined. Furthermore, it is shown that the Cheeger-Chern-Simons construction determines in a natural way $Aut^+P$-equivariant differential…

Conserved current for the Cotton tensor, black hole entropy and equivariant Pontryagin forms

- Physics
- 2010

The Chern–Simons Lagrangian density in the space of metrics of a three-dimensional manifold M is not invariant under the action of diffeomorphisms on M. However, its Euler–Lagrange operator can be…

Non-Hamiltonian Actions and Lie-Algebra Cohomology of Vector Fields

- Mathematics, Physics
- 2009

Two examples of Diff + S 1 -invariant closed two-forms obtained from forms on jet bundles, which does not admit equivariant moment maps are presented. The corresponding cohomological obstruction is…

Natural connections on the bundle of Riemannian metrics

- Mathematics
- 2005

Let \(FM,{\cal M}_M\) be the bundles of linear frames and Riemannian metrics of a manifold M, respectively. The existence of a unique Diff M-invariant connection form on \(J^1{\cal M}_M\times _M…

Symplectic structure and reduction on the space of Riemannian metrics

- Mathematics
- 2008

The space of Riemannian metrics $${\mathfrak{Met}}M$$ on an oriented compact manifold M of dimension n = 4k − 2 is endowed with a canonical presymplectic structure $$\omega $$ and a moment map…

Local Anomalies and Local Equivariant Cohomology

- Mathematics
- 2009

The locality conditions for the vanishing of local anomalies in field theory are shown to admit a geometrical interpretation in terms of local equivariant cohomology. This interpretation allows us to…

Equivariant differential characters and
Chern–Simons bundles

- Physics, MathematicsAlgebraic & Geometric Topology
- 2021

We construct Chern-Simons bundles as $\mathrm{Aut}^{+}P$-equivariant $U(1)$ -bundles with connection over the space of connections $\mathcal{A}_{P}$ on a principal $G$-bundle $P\rightarrow M$. We…

On the geometrical interpretation of locality in anomaly cancellation

- Journal of Geometry and Physics
- 2018

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Natural connections on the bundle of Riemannian metrics

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Let \(FM,{\cal M}_M\) be the bundles of linear frames and Riemannian metrics of a manifold M, respectively. The existence of a unique Diff M-invariant connection form on \(J^1{\cal M}_M\times _M…

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