Overview

The first five chapters of this book form an introductory course in piece­ wise-linear topology in which no assumptions are made other than basic topological notions. This course would be suitable as a second course in topology with a geometric flavour, to follow a first course in point-set topology, andi)erhaps to be given as a final year undergraduate course. The whole book gives an account of handle theory in a piecewise­ linear setting and could be the basis of a first year postgraduate lecture or reading course. Some results from algebraic topology are needed for handle theory and these are collected in an appendix. In a second appen­ dix are listed the properties of Whitehead torsion which are used in the s-cobordism theorem. These appendices should enable a reader with only basic knowledge to complete the book. The book is also intended to form an introduction to modern geo­ metric topology as a research subject, a bibliography of research papers being included. We have omittedacknowledgements and references from the main text and have collected these in a set of ""historical notes"" to be found after the appendices.

Full Product Details

Author:   Colin P. Rourke ,  B.J. Sanderson
Publisher:   Springer-Verlag Berlin and Heidelberg GmbH & Co. KG
Imprint:   Springer-Verlag Berlin and Heidelberg GmbH & Co. K
Edition:   Softcover reprint of the original 1st ed. 1982
Dimensions:   Width: 15.50cm , Height: 0.70cm , Length: 23.50cm
Weight:   0.220kg
ISBN:  

9783540111023

ISBN 10:   3540111026
Pages:   126
Publication Date:   01 January 1982
Audience:   Professional and scholarly ,  Professional & Vocational
Format:   Paperback
Publisher's Status:   Active
Availability:   Out of stock  
The supplier is temporarily out of stock of this item. It will be ordered for you on backorder and shipped when it becomes available.

Table of Contents

1. Polyhedra and P.L. Maps.- Basic Notation.- Joins and Cones.- Polyhedra.- Piecewise-Linear Maps.- The Standard Mistake.- P. L. Embeddings.- Manifolds.- Balls and Spheres.- The Poincaré Conjecture and the h-Cobordism Theorem..- 2. Complexes.- Simplexes.- Cells.- Cell Complexes.- Subdivisions.- Simplicial Complexes.- Simplicial Maps.- Triangulations.- Subdividing Diagrams of Maps.- Derived Subdivisions.- Abstract Isomorphism of Cell Complexes.- Pseudo-Radial Projection.- External Joins.- Collars.- Appendix to Chapter 2. On Convex Cells.- 3. Regular Neighbourhoods.- Full Subcomplexes.- Derived Neighbourhoods.- Regular Neighbourhoods.- Regular Neighbourhoods in Manifolds.- Isotopy Uniqueness of Regular Neighbourhoods.- Collapsing.- Remarks on Simple Homotopy Type.- Shelling.- Orientation.- Connected Sums.- Schönflies Conjecture.- 4. Pairs of Polyhedra and Isotopies.- Links and Stars.- Collars.- Regular Neighbourhoods.- Simplicial Neighbourhood Theorem for Pairs.- Collapsing and Shellingfor Pairs.- Application to Cellular Moves.- Disc Theorem for Pairs.- Isotopy Extension.- 5. General Position and Applications.- General Position.- Embedding and Unknotting.- Piping.- Whitney Lemma and Unlinking Spheres.- Non-Simply-Connected Whitney Lemma.- 6. Handle Theory.- Handles on a Cobordism.- Reordering Handles.- Handles of Adjacent Index.- Complementary Handles.- Adding Handles.- Handle Decompositions.- The CW Complex Associated with a Decomposition.- The Duality Theorems.- Simplifying Handle Decompositions.- Proof of the h-Cobordism Theorem.- The Relative Case.- The Non-Simply-Connected Case.- Constructing h-Cobordisms.- 7. Applications.- Unknotting Balls and Spheres in Codimension ? 3.- A Criterion for Unknotting in Codimension 2.- Weak 5-Dimensional Theorems.- Engulfing.- Embedding Manifolds.- Appendix A. Algebraic Results.- A. 1 Homology.- A. 2 Geometric Interpretation of Homology.- A. 3 Homology Groups of Spheres.- A. 4 Cohomology.- A. 5 Coefficients.- A. 6 Homotopy Groups.- A. 8 The Universal Cover.- Appendix B. Torsion.- B. 1 Geometrical Definition of Torsion.- B. 2 Geometrical Properties of Torsion.- B. 3 Algebraic Definition of Torsion.- B. 4 Torsion and Polyhedra.- B. 5 Torsion and Homotopy Equivalences.- Historical Notes.

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