The characteristic mapping of a foliated bundle

Parameter rigid actions of the Heisenberg groups

“…i A (dw) = d f i A (w) and is given by i A w(E(x)) = w(E). Nonsingular means that (i A w) x = 0 for some x ∈ M implies w = 0 (see [1,Example 1.5]). Let H * (F) be the leafwise cohomology of the foliated manifold (M, F) (see [1]).…”

“…Nonsingular means that (i A w) x = 0 for some x ∈ M implies w = 0 (see [1,Example 1.5]). Let H * (F) be the leafwise cohomology of the foliated manifold (M, F) (see [1]). Since i A : R (G * ) → (F) commutes with the differentials then it induces an injective linear mapping i A :…”

“…The cohomology of A is by definition the cohomology H * (G, C ∞ A (M)) of the G-module C ∞ A (M). Let F be the foliation given by the orbits of A and H 1 (F) be the first leafwise cohomology group of the foliated manifold (M, F) [1]. We prove in §1 (Proposition 1.2) that the first cohomology of A is isomorphic to H 1 (F).…”

On the Cohomology of Foliated Bundles

“…Reinhart in [16] appears naturally in the study of locally free actions of Lie groups and characteristic classes of foliations, [3], [17] and [18].…”

“…The cohomology of foliated manifolds appears naturally in the study of locally free actions of Lie groups and characteristic classes of foliations, [3], [17] and [18]. In this article we study the cohomology of foliated bundles F → (M, [14], [15] show that the cohomology H * (F) of a foliated bundle suspension of an action ϕ : Γ → Dif f (F ) is infinite dimensional for a large class of actions.…”