Group actions on dg-manifolds and their relation to equivariant cohomology

Details Group actions on dg-manifolds and their relation to equivariant cohomology Group actions on dg-manifolds and their relation to equivariant cohomology

2010-10-26

arxiv.org/abs/1010.5413v2

Mathematics

Differential Geometry

Section 3.2 improved. 35 pages

Scientific paper

Let G be a Lie group acting by diffeomorphisms on a manifold M and consider the image of T[1]G and T[1]M of G and M respectively in the category of differential graded manifolds. We show that the obstruction to lift the action of T[1]G on T[1]M to an action on a R[n]-bundle over T[1]M is measured by the G equivariant cohomology of M. We explicitly calculate the differential graded Lie algebra (dgla) of the symmetries of the R[n]-bundle over T[1]M and we use this dgla to understand which actions are hamiltonian.

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