In this paper we prove the equivalence of various algebraically or geometrically defined assembly maps used in formulating the main conjectures in K-and L-theory, and C *-theory.
This talk is based on joint work with Ronnie Lee and Mihail Tanase. We are interested in a kind of " rigidity " for finite group actions on certain smooth 4-manifolds, namely those constructed by connected sums of geometric pieces such as algebraic surfaces. We can ask how closely a smooth, orientation-preserving, finite group action on such a connected sum… (More)
The Göttingen State and University Library provides access to digitized documents strictly for noncommercial educational, research and private purposes and makes no warranty with regard to their use for other purposes. Some of our collections are protected by copyright. Publication and/or broadcast in any form (including electronic) requires prior written… (More)
We use the equivariant Yang-Mills moduli space to investigate the relation between the singular set, isotropy representations at fixed points, and permutation modules realized by the induced action on homol-ogy for smooth group actions on certain 4-manifolds.
In , two of us constructed a closed oriented 4-dimensional manifold with fundamental group Z that does not split off S 1 × S 3. In this note we show that this 4-manifold, and various others derived from it, do not admit smooth structures. Moreover, we find an infinite family of 4-manifolds with exactly the same properties. As a corollary, we obtain… (More)
In this paper, an explicit classification result for certain 5-manifolds with fundamental group Z/2 is obtained. These manifolds include total spaces of circle bundles over simply-connected 4-manifolds.
In this paper we show that the Farrell-Jones isomorphism conjectures are inherited in group extensions for assembly maps in algebraic K-theory and L-theory.
We describe the main steps in the calculation of surgery obstruction groups for finite groups. Some new results are given and extensive tables are included in the appendix. The surgery exact sequence of C. T. C. Wall  describes a method for classifying manifolds of dimension ≥ 5 within a given (simple) homotopy type, in terms of normal bundle… (More)
Suppose G is a p-hyperelementary group and R is a commutative ring such that the order of G is a unit in R. Suppose J is either one of Quillen's K-theory functors or one of Wall's oriented L-theory functors. We show that J(RG) can be detected by applying J(R?) to the subquotients of G such that all normal abelian subgroups are cyclic. In 3.A.6 we show that… (More)