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Piecewise Linear Topology
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Book Synopsis Introduction to Piecewise-Linear Topology by : Colin P. Rourke
Download or read book Introduction to Piecewise-Linear Topology written by Colin P. Rourke and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 133 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 omitted acknowledgements and references from the main text and have collected these in a set of "historical notes" to be found after the appendices.
Book Synopsis Piecewise Linear Topology by : John F. P. Hudson
Download or read book Piecewise Linear Topology written by John F. P. Hudson and published by . This book was released on 1969 with total page 304 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Piecewise Linear Structures On Topological Manifolds by : Yuli Rudyak
Download or read book Piecewise Linear Structures On Topological Manifolds written by Yuli Rudyak and published by World Scientific. This book was released on 2015-12-28 with total page 129 pages. Available in PDF, EPUB and Kindle. Book excerpt: The study of triangulations of topological spaces has always been at the root of geometric topology. Among the most studied triangulations are piecewise linear triangulations of high-dimensional topological manifolds. Their study culminated in the late 1960s-early 1970s in a complete classification in the work of Kirby and Siebenmann. It is this classification that we discuss in this book, including the celebrated Hauptvermutung and Triangulation Conjecture.The goal of this book is to provide a readable and well-organized exposition of the subject, which would be suitable for advanced graduate students in topology. An exposition like this is currently lacking.
Book Synopsis Introduction to Piecewise-linear Topology by : Colin Patrick Rourke
Download or read book Introduction to Piecewise-linear Topology written by Colin Patrick Rourke and published by . This book was released on 1970 with total page 123 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Introduction to Piecewise-linear Topology by : Colin Patrick Rourke
Download or read book Introduction to Piecewise-linear Topology written by Colin Patrick Rourke and published by Springer. This book was released on 1972 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Introduction to Piecewise-Linear Topology by : Colin P Rourke
Download or read book Introduction to Piecewise-Linear Topology written by Colin P Rourke and published by . This book was released on 1972-11-16 with total page 136 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Smoothings of Piecewise Linear Manifolds by : Morris W. Hirsch
Download or read book Smoothings of Piecewise Linear Manifolds written by Morris W. Hirsch and published by Princeton University Press. This book was released on 1974-10-21 with total page 152 pages. Available in PDF, EPUB and Kindle. Book excerpt: The intention of the authors is to examine the relationship between piecewise linear structure and differential structure: a relationship, they assert, that can be understood as a homotopy obstruction theory, and, hence, can be studied by using the traditional techniques of algebraic topology. Thus the book attacks the problem of existence and classification (up to isotopy) of differential structures compatible with a given combinatorial structure on a manifold. The problem is completely "solved" in the sense that it is reduced to standard problems of algebraic topology. The first part of the book is purely geometrical; it proves that every smoothing of the product of a manifold M and an interval is derived from an essentially unique smoothing of M. In the second part this result is used to translate the classification of smoothings into the problem of putting a linear structure on the tangent microbundle of M. This in turn is converted to the homotopy problem of classifying maps from M into a certain space PL/O. The set of equivalence classes of smoothings on M is given a natural abelian group structure.
Book Synopsis Grassmannians and Gauss Maps in Piecewise-Linear Topology by : Norman Levitt
Download or read book Grassmannians and Gauss Maps in Piecewise-Linear Topology written by Norman Levitt and published by Springer. This book was released on 2006-11-14 with total page 208 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book explores the possibility of extending the notions of "Grassmannian" and "Gauss map" to the PL category. They are distinguished from "classifying space" and "classifying map" which are essentially homotopy-theoretic notions. The analogs of Grassmannian and Gauss map defined incorporate geometric and combinatorial information. Principal applications involve characteristic class theory, smoothing theory, and the existence of immersion satifying certain geometric criteria, e.g. curvature conditions. The book assumes knowledge of basic differential topology and bundle theory, including Hirsch-Gromov-Phillips theory, as well as the analogous theories for the PL category. The work should be of interest to mathematicians concerned with geometric topology, PL and PD aspects of differential geometry and the geometry of polyhedra.
Book Synopsis Smoothings of Piecewise Linear Manifolds. (AM-80), Volume 80 by : Morris W. Hirsch
Download or read book Smoothings of Piecewise Linear Manifolds. (AM-80), Volume 80 written by Morris W. Hirsch and published by Princeton University Press. This book was released on 2016-03-02 with total page 149 pages. Available in PDF, EPUB and Kindle. Book excerpt: The intention of the authors is to examine the relationship between piecewise linear structure and differential structure: a relationship, they assert, that can be understood as a homotopy obstruction theory, and, hence, can be studied by using the traditional techniques of algebraic topology. Thus the book attacks the problem of existence and classification (up to isotopy) of differential structures compatible with a given combinatorial structure on a manifold. The problem is completely "solved" in the sense that it is reduced to standard problems of algebraic topology. The first part of the book is purely geometrical; it proves that every smoothing of the product of a manifold M and an interval is derived from an essentially unique smoothing of M. In the second part this result is used to translate the classification of smoothings into the problem of putting a linear structure on the tangent microbundle of M. This in turn is converted to the homotopy problem of classifying maps from M into a certain space PL/O. The set of equivalence classes of smoothings on M is given a natural abelian group structure.
Book Synopsis Piecewise Linear Structures on Topological Manifolds by :
Download or read book Piecewise Linear Structures on Topological Manifolds written by and published by . This book was released on 2001 with total page 72 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis A CONSTRUCTIVE VERSION OF PIECEWISE LINEAR TOPOLOGY.. by : Cynthia Ann Blocher Brown
Download or read book A CONSTRUCTIVE VERSION OF PIECEWISE LINEAR TOPOLOGY.. written by Cynthia Ann Blocher Brown and published by . This book was released on 1977 with total page 161 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Piecewise Linear Topology by : John F. B. Hudson
Download or read book Piecewise Linear Topology written by John F. B. Hudson and published by . This book was released on 1969 with total page 282 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Geometric Topology in Dimensions 2 and 3 by : E.E. Moise
Download or read book Geometric Topology in Dimensions 2 and 3 written by E.E. Moise and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 272 pages. Available in PDF, EPUB and Kindle. Book excerpt: Geometric topology may roughly be described as the branch of the topology of manifolds which deals with questions of the existence of homeomorphisms. Only in fairly recent years has this sort of topology achieved a sufficiently high development to be given a name, but its beginnings are easy to identify. The first classic result was the SchOnflies theorem (1910), which asserts that every 1-sphere in the plane is the boundary of a 2-cell. In the next few decades, the most notable affirmative results were the "Schonflies theorem" for polyhedral 2-spheres in space, proved by J. W. Alexander [Ad, and the triangulation theorem for 2-manifolds, proved by T. Rad6 [Rd. But the most striking results of the 1920s were negative. In 1921 Louis Antoine [A ] published an extraordinary paper in which he 4 showed that a variety of plausible conjectures in the topology of 3-space were false. Thus, a (topological) Cantor set in 3-space need not have a simply connected complement; therefore a Cantor set can be imbedded in 3-space in at least two essentially different ways; a topological 2-sphere in 3-space need not be the boundary of a 3-cell; given two disjoint 2-spheres in 3-space, there is not necessarily any third 2-sphere which separates them from one another in 3-space; and so on and on. The well-known "horned sphere" of Alexander [A ] appeared soon thereafter.
Book Synopsis Piecewise Linear Topology by : John F. P. Hudson
Download or read book Piecewise Linear Topology written by John F. P. Hudson and published by . This book was released on 1969 with total page 282 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis A Grassmannian for Piecewise Linear Topology by : Regina Hunter Mladineo
Download or read book A Grassmannian for Piecewise Linear Topology written by Regina Hunter Mladineo and published by . This book was released on 1979 with total page 116 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Foundational Essays on Topological Manifolds, Smoothings, and Triangulations by : Robion C. Kirby
Download or read book Foundational Essays on Topological Manifolds, Smoothings, and Triangulations written by Robion C. Kirby and published by Princeton University Press. This book was released on 1977-05-21 with total page 376 pages. Available in PDF, EPUB and Kindle. Book excerpt: Since Poincaré's time, topologists have been most concerned with three species of manifold. The most primitive of these--the TOP manifolds--remained rather mysterious until 1968, when Kirby discovered his now famous torus unfurling device. A period of rapid progress with TOP manifolds ensued, including, in 1969, Siebenmann's refutation of the Hauptvermutung and the Triangulation Conjecture. Here is the first connected account of Kirby's and Siebenmann's basic research in this area. The five sections of this book are introduced by three articles by the authors that initially appeared between 1968 and 1970. Appendices provide a full discussion of the classification of homotopy tori, including Casson's unpublished work and a consideration of periodicity in topological surgery.
Book Synopsis General Position and Structural Stability in Piecewise Linear Topology by : David Allen Singer
Download or read book General Position and Structural Stability in Piecewise Linear Topology written by David Allen Singer and published by . This book was released on 1970 with total page 142 pages. Available in PDF, EPUB and Kindle. Book excerpt:
