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

Two examples of $\mathrm{Diff}^+S^1$-invariant closed two-forms obtained from forms on jet bundles, which does not admit equivariant moment maps are presented. The corresponding cohomological obstruction is computed and shown to coincide with a nontrivial Lie algebra cohomology class on $H^2(\mathfrak{X}(S^1))$

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

The Chern-Simons lagrangian density in the space of metrics of a 3-dimensional manifold M is not invariant under the action of diffeomorphisms on M. However, its Euler-Lagrange operator can be identified with the Cotton tensor, which is invariant under diffeomorphims. As the lagrangian is not invariant, Noether Theorem cannot be applied to obtain conserved currents. We show that it is possible to obtain an equivariant conserved current for the Cotton tensor by using the first equivariant Pontryagin form on the bundle of metrics. Finally we define a hamiltonian current which gives the contribution of the Chern-Simons term to the black hole entropy, energy and angular momentum.Comment: 13 page

Local Anomalies, Local Equivariant Cohomology and the Variational Bicomplex

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, thus providing a method to deal with the problem of locality in the geometrical approaches to the study of local anomalies based on the Atiyah-Singer index theorem. The local cohomology is shown to be related to the cohomology of jet bundles by means of the variational bicomplex theory. Using these results and the techniques for the computation of the cohomology of invariant variational bicomplexes in terms of relative Gel'fand-Fuks cohomology introduced in [6], we obtain necessary and sufficient conditions for the cancellation of local gravitational and mixed anomalies.Comment: 36 pages. The paper is divided in two part

Self-study introduction course of financial mathematics with excel

El objetivo de este proyecto es diseñar un curso introductorio a Excel para la asignatura Financial Mathematics del grupo en inglés del Grado en Administración y Dirección de Empresas, al objeto de crear un material ad hoc de autoaprendizaje para dicho grupo.Depto. de Economía Financiera y Actuarial y EstadísticaFac. de Ciencias Económicas y EmpresarialesFALSEsubmitte