Cancellation of hyperbolic forms and topological four-manifolds.
Centralizers of gap groups
A finite group G is called a gap group if there exists an ℝG-module which has no large isotropy groups except at zero and satisfies the gap condition. The gap condition facilitates the process of equivariant surgery. Many groups are gap groups and also many groups are not. In this paper, we clarify the relation between a gap group and the structures of its centralizers. We show that a nonsolvable group which has a normal, odd prime power index proper subgroup is a gap group.
Class numbers and periodic smooth maps.
Classification of free actions by some metacyclic groups on
Close PL involutions of 3-manifolds have close fixed point sets: 1-dimensional components
Close PL involutions of 3-manifolds which are conjugate by a small homeomorphism
Cohomology and group actions.
Cohomology and Group Actions.
Commuting involutions whose fixed point set consists of two special components
Let Fⁿ be a connected, smooth and closed n-dimensional manifold. We call Fⁿ a manifold with property when it has the following property: if is any smooth closed m-dimensional manifold with m > n and is a smooth involution whose fixed point set is Fⁿ, then m = 2n. Examples of manifolds with this property are: the real, complex and quaternionic even-dimensional projective spaces , and , and the connected sum of and any number of copies of Sⁿ × Sⁿ, where Sⁿ is the n-sphere and n is not...
Computing Adams operations on the Burnside ring of a finite group.
Cyclic actions on - and -bundles over
Cyclic branched coverings and homology 3-spheres with large group actions
We show that, if the covering involution of a 3-manifold M occurring as the 2-fold branched covering of a knot in the 3-sphere is contained in a finite nonabelian simple group G of diffeomorphisms of M, then M is a homology 3-sphere and G isomorphic to the alternating or dodecahedral group 𝔸₅ ≅ PSL(2,5). An example of such a 3-manifold is the spherical Poincaré sphere. We construct hyperbolic analogues of the Poincaré sphere. We also give examples of hyperbolic ℤ₂-homology 3-spheres with PSL(2,q)-actions,...
Cyclic group actions on odd-dimensional spheres.