Surgery on Piecewise Linear Manifolds and Applications by William Browder and Morris

A Splitting Theorem for Manifolds and Surgery Groups

I. In this paper we state a splitting theorem for manifolds and describe some applications and consequences. We announced a weaker form of this result in August 1969 at the Georgia Topology Conference. Besides its immediate applications, especially in the classification of homotopy equivalent manifolds, it implies the existence of a Mayer-Vietoris sequence for surgery groups. Using this, many s...

Three-manifolds with Fundamental Group a Free Product by William Jaco

DIFFERENTIABLE STRUCTURES 1. Classification of Manifolds

(1) Classify all spaces ludicrously impossible. (2) Classify manifolds only provably impossible (because any finitely presented group is the fundamental group of a 4-manifold, and finitely presented groups are not able to be classified). (3) Classify manifolds with a given homotopy type (sort of worked out in 1960’s by Wall and Browder if π1 = 0. There is something called the Browder-Novikov-Su...

The Classification of Simple Spin-manifolds in Dimension Eight

We provide an elementary proof for the classification of certain piecewise linear manifolds of dimension eight which was conjectured by Stefan Müller [13]. Our proof is based on minimal handle presentations according to Smale and several explicit computations involving surgery and the classification of links. It illustrates the geometric meaning of the algebro-topological data associated with t...

Manifolds with Tti

In this note we announce some results extending results of S. P. Novikov ([6] and [7]), the author [2], and C. T. C. Wall [8]. In the above papers it is shown how to characterize the homotopy type of 1-connected smooth closed manifolds of dimension w ^ S , « ^ 2 mod 4, and how to reduce the diffeomorphy classification of such manifolds to homotopy theory, with similar results for bounded manifo...