On finite cocycles and the sphere theorem
On finite groups acting on a connected sum of 3-manifolds S² × S¹
Let denote the closed 3-manifold obtained as the connected sum of g copies of S² × S¹, with free fundamental group of rank g. We prove that, for a finite group G acting on which induces a faithful action on the fundamental group, there is an upper bound for the order of G which is quadratic in g, but there does not exist a linear bound in g. This implies then a Jordan-type bound for arbitrary finite group actions on which is quadratic in g. For the proofs we develop a calculus for finite group...
On finite groups acting on acyclic complexes of dimension two.
We conjecture that every finite group G acting on a contractible CW-complex X of dimension 2 has at least one fixed point. We prove this in the case where G is solvable, and under this additional hypothesis, the result holds for X acyclic.
On finite groups acting on acyclic low-dimensional manifolds
We consider finite groups which admit a faithful, smooth action on an acyclic manifold of dimension three, four or five (e.g. Euclidean space). Our first main result states that a finite group acting on an acyclic 3- or 4-manifold is isomorphic to a subgroup of the orthogonal group O(3) or O(4), respectively. The analogous statement remains open in dimension five (where it is not true for arbitrary continuous actions, however). We prove that the only finite nonabelian simple groups admitting a smooth...
On finite groups of isometries of handlebodies in arbitrary dimensions and finite extensions of Schottky groups
It is known that the order of a finite group of diffeomorphisms of a 3-dimensional handlebody of genus g > 1 is bounded by the linear polynomial 12(g-1), and that the order of a finite group of diffeomorphisms of a 4-dimensional handlebody (or equivalently, of its boundary 3-manifold), faithful on the fundamental group, is bounded by a quadratic polynomial in g (but not by a linear one). In the present paper we prove a generalization for handlebodies of arbitrary dimension d, uniformizing handlebodies...
On finite subgroups of groups of type VF.
On finite type 3-mainfold invarinats II.
On Finsler-Weyl manifolds and connections
Let be a manifold with all structures smooth which admits a metric . Let be a linear connection on such that the associated covariant derivative satisfies for some 1-form on . Then one refers to the above setup as a Weyl structure on and says that the pair fits . If and if fits , then fits . Thus if one thinks of this as a map , then .In this paper, the author attempts to apply Weyl’s idea above to Finsler spaces. A Finsler fundamental function satisfies (i) for...
On fixed point free involutions of
On foliations in Sikorski differential spaces with Brouwerian leaves
The class of locally connected and locally homeomorphically homogeneous topological spaces such that every one-to-one continuous mapping of an open subspace into the space is open has been considered. For a foliation F [3] on a Sikorski differential space M with leaves having the above properties it is proved that for some open sets U in M covering the set of all points of M the connected components of U ∩ L̲ in the topology of M coincide with the connected components in the topology of L for L∈...
On foliations of ... By minimal hypersurfaces.
On foliations of differential spaces
On foliations with coregular factor mapping
On foliations with leaves satisfying some geometrical conditions [Book]
On for dimensional s-cobordisms, II.
On Formal Groups and Singularities in Complex Corbordism Theory.
On Four Dimensional Surgery and Applications
On Fox's theory of overlays
On Framed Cobordism Classes Representable on a Fixed Manifold.
On framed links of Peiffer identities