On the finiteness obstruction of certain periodic groups.
On the first homology of automorphism groups of manifolds with geometric structures
Hermann and Thurston proved that the group of diffeomorphisms with compact support of a smooth manifold M which are isotopic to the identity is a perfect group. We consider the case where M has a geometric structure. In this paper we shall survey on the recent results of the first homology of the diffeomorphism groups which preserve a smooth G-action or a foliated structure on M. We also work in Lipschitz category.
On the form of principal torus-bundles over toruses
On the four-dimensional -manifolds of positive Ricci curvature.
On the genus of represenattion spheres.
On the geometric topology of locally linear actions of finite groups
On the Geometric Weight System of Differentiable Compact Transformation Groups on Acyclic Manifolds.
On the G-spaces having an -G-CW-approximation by a G-CW-complex of finite G-type
On the Hantzsche-Wendt Manifold.
On the homeomorphism groups of manifolds and their universal coverings
Let H c(M) stand for the path connected identity component of the group of all compactly supported homeomorphisms of a manifold M. It is shown that H c(M) is perfect and simple under mild assumptions on M. Next, conjugation-invariant norms on Hc(M) are considered and the boundedness of Hc(M) and its subgroups is investigated. Finally, the structure of the universal covering group of Hc(M) is studied.
On the Homology of Finite Free (Z/2)n-Complexes.
On the homotopy groups of some equivariant automorphism groups of spheres
On the homotopy theory of equivariant automorphism groups.
On the homotopy type of and connected problems
This paper reports on some results concerning:a) The homotopy type of the group of diffeomorphisms of a differentiable compact manifold (with -topology).b) the result of the homotopy comparison of this space with the group of all homeomorphisms Homeo (with -topology). As a biproduct, one gets new facts about the homotopy groups of , and about the number of connected components of the space of topological and combinatorial pseudoisotopies.The results are contained in Section 1 and Section...
On the Index of Approximating Sets of Periodic Points.
On the linearization theorem for proper Lie groupoids
We revisit the linearization theorems for proper Lie groupoids around general orbits (statements and proofs). In the fixed point case (known as Zung’s theorem) we give a shorter and more geometric proof, based on a Moser deformation argument. The passage to general orbits (Weinstein) is given a more conceptual interpretation: as a manifestation of Morita invariance. We also clarify the precise statements of the Linearization Theorem (there has been some confusion on this, which has propagated throughout...
On the non-existence of certain group topologies
Minimal Hausdorff (Baire) group topologies of certain groups of transformations naturally occurring in analysis are studied. The results obtained are subsequently applied to show that, e.g., the homeomorphism groups of the rational and of the irrational numbers carry no Polish group topology. In answer to a question of A. S. Kechris it is shown that the group of Borel automorphisms of ℝ cannot be a Polish group either.
On the Orbit Structures of SU (n)-Actions on Manifolds of the Type of Euclidean, Spherical or Projective Spaces.
On the Rank of Abelian Groups Acting Freely on (Sn)k.
On the Segal conjecture for compact Lie groups.