Eine Bemerkung zur topologischen Entropie.
The aim of this paper is to prove that a control affine system on a manifold is equivalent by diffeomorphism to a linear system on a Lie group or a homogeneous space if and only if the vector fields of the system are complete and generate a finite dimensional Lie algebra. A vector field on a connected Lie group is linear if its flow is a one parameter group of automorphisms. An affine vector field is obtained by adding a left invariant one. Its projection on a homogeneous space, whenever it exists,...
Let be a topological group. We give the existence of an equivariant homology and cohomology theory, defined on the category of all -pairs and -maps, which both satisfy all seven equivariant Eilenberg-Steenrod axioms and have a given covariant and contravariant, respectively, coefficient system as coefficients.In the case that is a compact Lie group we also define equivariant -complexes and mention some of their basic properties.The paper is a short abstract and contains no proofs.
We consider locally standard 2-torus manifolds, which are a generalization of small covers of Davis and Januszkiewicz and study their equivariant classification. We formulate a necessary and sufficient condition for two locally standard 2-torus manifolds over the same orbit space to be equivariantly homeomorphic. This leads us to count the equivariant homeomorphism classes of locally standard 2-torus manifolds with the same orbit space.