The Geometric Topology of 3-manifolds, Volume 40
This book belongs in both graduate and undergraduate libraries as a useful reference for students and researchers in topology. It is directed toward mathematicians interested in geometry who have had at least a beginning course in topology. It should provide the reader with a better understanding of the physical properties of Euclidean 3-space--the space in which we presume we live. The reader should learn of some unsolved problems that continue to baffle reseachers. The most profound result in the volume is the side approximation theorem. However, some of the preliminary results and some of the applications may be used more frequently for reference.
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PL Planar Maps
The Schoenflies Theorem
the Generalized Schoenflies Theorem
The Fundamental Group
Mapping onto Spheres
Intersections of Surfaces with 1Simplexes
Intersections of Surfaces with Skeleta
Side Approximation Theorem
The PL Schoenflies Theorem for R³
The Loop Theorem
Pulling Back Feelers
2-sphere in R3 3-manifold 3-manifold-with-boundary Alexander horned sphere Antoine's necklace Bd A2 Bd A3 Bd B3 Bd D2 Bing bounded branch point C(Bd cellular Chapter closed set closed subset complement component of K2 cone contains covering space crumpled cube Dehn's lemma denote diameter less double lines elements equivalence class extended feelers finite number follows from Theorem fundamental group homeomor homotopy identity Int A2 interior lies linear locally connected loop theorem metric space mutually disjoint neighborhood no-triod property nonsingular disk normal Dehn disk odd number open set open subset PL arc PL disk PL homeomorphism PL Schoenflies theorem plane Poincare conjecture point in R3 polygon polyhedral proof of Theorem push S2 n A2 S2 n Bd separates shelled shown in Figure shrunk simple closed curve simplex simply-connected singular disk spanning arc subdivision Suppose topological triangulation triple points undercrossing union vertex vertices wild 2-sphere