Many topological problems can be solved by using either combinatorial or differential methods. The main goal of this text is to advance as far as possible in the study of the properties of topological spaces (especially manifolds) without employing complicated techniques.
"Modern topology uses very diverse methods. This book is devoted largely to methods of combinatorial topology, which reduce the study of topological spaces to investigations of their partitions into elementary sets, and to methods of differential topology, which deal with smooth…
Introduction -- Mathematics of Steve Armentrout: A review / S. Singh -- Bing's dogbone space is not strongly locally simply connected / S. Armentrout -- A program for the Poincare conjecture and some of its ramifications / V. Poenaru -- On the foundation of geometry, analysis, a…
Recent success with the four-dimensional Poincare conjecture has revived interest in low-dimensional topology, especially the three-dimensional Poincare conjecture and other aspects of the problems of classifying three-dimensional manifolds. These problems have a driving force, …
