Classification of {${\rm SO}(3)$}-actions on five manifolds

On the Classification of Transitive Effective Actions on Stiefel Manifolds

Introduction. Let G be a compact connected Lie group and H a closed subgroup of G. Then the coset space G/H is a smooth manifold with G acting transitively as translations. It is easy to see that the natural action of G on G/H is effective if and only if H contains no nontrivial normal subgroup of G. For a given compact homogeneous space M=G/H, one might ask whether there are any other (differe...

Actions on Manifolds from Deformations

Classification of Multiplicity Free Hamiltonian Actions of Complex Tori on Stein Manifolds

A Hamiltonian action of a complex torus on a symplectic complex manifold is said to be multiplicity free if a general orbit is a lagrangian submanifold. To any multiplicity free Hamiltonian action of a complex torus T ∼= (C) on a Stein manifold X we assign a certain 5-tuple consisting of a Stein manifold Y , an étale map Y → t, a set of divisors on Y and elements of H(Y, Z), H(Y, C). We show th...

TORUS AND Z/p ACTIONS ON MANIFOLDS

Let G be either a finite cyclic group of prime order or S. We show that if G acts on a manifold or, more generally, on a Poincaré duality space M , then each term of the Leray spectral sequence of the map M×GEG → BG satisfies a properly defined “Poincaré duality.” As a consequence of this fact we obtain new results relating the cohomology groups of M and M. We apply our results to study group a...

Homologically Trivial Group Actions on 4-Manifolds

In this paper we investigate pseudofree homologically trivial actions of arbitrary finite groups on simply connected 4-manifolds. It turns out that there are surprisingly strong restrictions on the groups and on the actions, especially when one considers the fact that any finite group can act, even freely, on some simply connected 4-manifold. Recall that a finite group action is free if no nont...