Topology Seminar Wisconsin, 1965. (AM-60), Volume 60 (Annals of Mathematics Studies)

During the summer of 1965, an informal seminar in geometric topology was held at the University of Wisconsin under the direction of Professor Bing. Twenty-five of these lectures are included in this study, among them Professor Bing's lecture describing the recent attacks of Haken and Poincaré on the Poincaré conjectures, and sketching a proof of Haken's main result. CONTENTS Preface CHAPTER I: 3-Manifolds MONOTONE DECOMPOSITIONS OF E^3 EQUIVALENT DECOMPOSITIONS OF E^3 ANOTHER DECOMPOSITION OF E^3 INTO POINTS AND INTERVALS CRUMPLED CUBES SEWINGS OF CRUMPLED CUBES WHICH DO NOT YIELD S^3 CANONICAL NEIGHBORHOODS IN THREE-MANIFOLDS BOUNDARY LINKS SURFACES IN E^3 ADDITIONAL QUESTIONS ON 3-MANIFOLDS CHAPTER II: The Poincaré Conjecture NOW NOT TO PROVE THE POINCARÉ CONJECTURE MAPPING A 3-SPHERE ONTO A HOMOTOPY 3-SPHERE CONCERNING FAKE CUBES CHAPTER III: ON CERTAIN FIRST COUNTABLE SPACES REMARKS ON THE NORMAL MOORE SPACE METRIZATION PROBLEM TWO CONJECTURES IN POINT SET THEORY ALMOST CONTINUOUS FUNCTIONS AND FUNCTIONS OF BAIRE CLASS 1 CHAINABLE CONTINUA THE EXISTENCE OF A COMPLETE METRIC FOR A SPECIAL MAPPING SPACE AND SOME CONSEQUENCES FINITE DIMENSIONAL SUBSETS OF INFINITE DIMENSIONAL SPACES TYPES OF ULTRAFILTERS ADDITIONAL QUESTIONS ON ABSTRACT SPACES CHAPTER IV: N-manifolds TAMING POLYHEDRA IN THE TRIVIAL RANGE SOME NICE EMBEDDINGS IN THE TRIVIAL RANGE APPROXIMATIONS AND ISOTOPIES IN THE TRIVIAL RANGE ON ASPHERICAL EMBEDDINGS OF 2-SPHERES IN THE 4-SPHERE GEOMETRIC CHARACTERIZATION OF DIFFERENTIABLE MANIFOLDS IN EUCLIDEAN SPACE WHITEHEAD TORSION AND h-COBORDISM ADDITIONAL QUESTIONS ON N-MANIFOLDS COMPLETELY REGULAR MAPPINGS, FIBER SPACES, THE WEAK BUNDLE PROPERTIES AND THE GENERALIZED SLICING STRUCTURE PROPERTIES FIBER SPACES AND n-REGULARITY FIBER SPACES WITH TOTALLY PATHWISE DISCONNECTED FIBERS SOME QUESTIONS IN THE THEORY OF NORMAL FIBER SPACES FOR TOPOLOGICAL MANIFOLDS