Topological obstructions to certain Lie group actions on manifolds

Topological Obstructions to Certain Lie Group Actions on Manifolds

Given a smooth closed S1-manifold M , this article studies the extent to which certain numbers of the form (f∗ (x) · P · C) [M ] are determined by the fixed-point set MS 1 , where f : M → K (π1 (M) , 1) classifies the universal cover of M , x ∈ H∗ (π1 (M) ;Q), P is a polynomial in the Pontrjagin classes of M , and C is in the subalgebra of H∗ (M ;Q) generated by H2 (M ;Q). When MS 1 = ∅, variou...

Topological Centers of Certain Banach Module Actions

Integrability of certain distributions associated to actions on manifolds and an introduction to Lie-algebraic control

Results are given on the integrability of certain distributions which arise from smoothly parametrized families of diffeomorphisms acting on manifolds. Applications to control problems and in particular to the problem of sampling are discussed.

Erratum: Topological Centres of Certain Banach Module Actions

Lie group actions on compact

Let G be a homotopically trivial and effective compact Lie group action on a compact manifold N of nonpositive curvature. Under certain assumptions on N we prove that if G has dimension equal to rank of Center π1(N), then G must be connected. Furthermore, if on N there exists a point having negative definite Ricci tensor, then we show that G is the trivial group.