Secondary Invariants for Families of Bundles

By Rune Ljungmann
PhD Dissertations
September 2006
Abstract:

This thesis is concerned with aspects of the construction of secondary invariants for families of bundles.

The usual procedure for constructing invariants for families of bundles is to take the ordinary characteristic classes of the total bundle and push them forward to the cohomology of the parameter space.

In order to construct secondary classes for families of bundles, we need a procedure for integration along the fibres in smooth Deligne cohomology. In the first part of the thesis, such a map is constructed using simplicial forms.

In the second part of the thesis, this integration map is applied to the construction of secondary invariants for certain symplectic fibrations with connection. These classes extend the characteristic classes for hamiltonian bundles constructed by Reznikov.

The thesis also contains an explicit construction of some characteristic classes for symplectic surface bundles, which existence was proven by Kotschick and Morita.

Thesis advisor: Johan L. Dupont
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