Spin(4) actions on $8$-dimensional manifolds (I)

GROUP ACTIONS ON SPIN MANIFOLDS(i)

A generalization of the theorem of V. Bargmann concerning unitary and ray representations is obtained and is applied to the general problem of lifting group actions associated to the extension of structure of a bundle. In particular this is applied to the Poincare group ? of a Lorentz manifold M. It is shown that the topological restrictions needed to lift an action in ? are more stringent than...

Proper Actions of High-Dimensional Groups on Complex Manifolds

We explicitly classify all pairs (M,G), where M is a connected complex manifold of dimension n ≥ 2 and G is a connected Lie group acting properly and effectively on M by holomorphic transformations and having dimension dG satisfying n 2 + 2 ≤ dG < n 2 + 2n. These results extend – in the complex case – the classical description of manifolds admitting proper actions of groups of sufficiently high...

Semi-free Hamiltonian Circle Actions on 6 Dimensional Symplectic Manifolds

Assume (M,ω) is a connected, compact 6 dimensional symplectic manifold equipped with a semi-free Hamiltonian circle action, such that the fixed point set consists of isolated points or compact orientable surfaces. We restrict attention to the case dim H(M) < 3. We give a complete list of the possible manifolds, determine their equivariant cohomology ring and equivariant Chern classes. Some of t...

Actions of the Torus on 4-manifolds. I

Smooth actions of the 2-dimensional torus group SO(2) x 50(2) on smooth, closed, orientable 4-manifolds are studied. A cross-sectioning theorem for actions without finite nontrivial isotropy groups and with either fixed points or orbits with isotropy group isomorphic to SO(2) yields an equivariant classification for these cases. This classification is made numerically specific in terms of orbit...

Actions on Manifolds from Deformations