ar X iv : d g - ga / 9 61 00 15 v 2 2 8 O ct 1 99 6 EQUIVARIANT NOVIKOV INEQUALITIES
نویسندگان
چکیده
We establish an equivariant generalization of the Novikov inequalities which allow to estimate the topology of the set of critical points of a closed basic invariant form by means of twisted equivariant cohomology of the manifold. We apply these inequalities to study cohomology of the fixed points set of a symplectic torus action. We show that in this case our inequalities are perfect, i.e. they are in fact equalities. In [N1,N2] S.P.Novikov associated to any real cohomology class ξ ∈ H(M,R) of a closed manifold M a sequence of integers β0(ξ), . . . , βn(ξ) (where n = dimM) and then it was shown that for any closed 1-form θ on M , having non-degenerate critical points, the Morse numbers mp(θ) satisfy the following inequalities
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ar X iv : d g - ga / 9 61 00 15 v 1 2 6 O ct 1 99 6 EQUIVARIANT NOVIKOV INEQUALITIES
We establish an equivariant generalization of the Novikov inequalities which allow to estimate the topology of the set of critical points of a closed basic invariant form by means of twisted equivariant cohomology of the manifold. We apply these inequalities to study cohomology of the fixed points set of a symplectic torus action. We show that in this case our inequalities are perfect, i.e. the...
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