Piecewise Linear Structures On Topological Manifolds
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Piecewise Linear Structures On Topological Manifolds
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Author : Yuli RUDYAK
language : en
Publisher: World Scientific
Release Date : 2015-12-28
Piecewise Linear Structures On Topological Manifolds written by Yuli RUDYAK and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-12-28 with Mathematics categories.
"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."--
Piecewise Linear Structures On Topological Manifolds
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Author :
language : en
Publisher:
Release Date : 2001
Piecewise Linear Structures On Topological Manifolds written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001 with categories.
Smoothings Of Piecewise Linear Manifolds
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Author : Morris W. Hirsch
language : en
Publisher: Princeton University Press
Release Date : 1974-10-21
Smoothings Of Piecewise Linear Manifolds written by Morris W. Hirsch and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1974-10-21 with Mathematics categories.
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.
Smoothings Of Piecewise Linear Manifolds Am 80 Volume 80
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Author : Morris W. Hirsch
language : en
Publisher: Princeton University Press
Release Date : 2016-03-02
Smoothings Of Piecewise Linear Manifolds Am 80 Volume 80 written by Morris W. Hirsch and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-03-02 with Mathematics categories.
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.
Piecewise Linear Structures On Topological Manifolds
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Author : Yuli Rudyak
language : en
Publisher: World Scientific
Release Date : 2015-12-28
Piecewise Linear Structures On Topological Manifolds written by Yuli Rudyak and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-12-28 with Mathematics categories.
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.
Introduction To Piecewise Linear Topology
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Author : Colin Patrick Rourke
language : en
Publisher: Springer
Release Date : 1972-11-16
Introduction To Piecewise Linear Topology written by Colin Patrick Rourke and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 1972-11-16 with Mathematics categories.
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.
Piecewise Linear Topology
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Author : John F. P. Hudson
language : en
Publisher:
Release Date : 1969
Piecewise Linear Topology written by John F. P. Hudson and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1969 with Piecewise linear topology categories.
Classification Of Smooth And Piecewise Linear Manifolds Structures Using The Product Structure Theorem
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Author : Rc Kirby
language : en
Publisher:
Release Date : 1972
Classification Of Smooth And Piecewise Linear Manifolds Structures Using The Product Structure Theorem written by Rc Kirby and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1972 with categories.
Topological Library
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Author : Sergeĭ Petrovich Novikov
language : en
Publisher: World Scientific
Release Date : 2010
Topological Library written by Sergeĭ Petrovich Novikov and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010 with Mathematics categories.
1. On manifolds homeomorphic to the 7-sphere / J. Milnor -- 2. Groups of homotopy spheres. I / M. Kervaire and J. Milnor -- 3. Homotopically equivalent smooth manifolds / S.P. Novikov -- 4. Rational Pontrjagin classes. Homeomorphism and homotopy type of closed manifolds / S.P. Novikov -- 5. On manifolds with free abelian fundamental group and their applications (Pontrjagin classes, smooth structures, high-dimensional knots) / S.P. Novikov -- 6. Stable homeomorphisms and the annulus conjecture / R. Kirby
Topological Library Part 2 Characteristic Classes And Smooth Structures On Manifolds
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Author : Serguei Petrovich Novikov
language : en
Publisher: World Scientific
Release Date : 2009-10-07
Topological Library Part 2 Characteristic Classes And Smooth Structures On Manifolds written by Serguei Petrovich Novikov and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-10-07 with Mathematics categories.
This is the second of a three-volume set collecting the original and now-classic works in topology written during the 1950s-1960s. The original methods and constructions from these works are properly documented for the first time in this book. No existing book covers the beautiful ensemble of methods created in topology starting from approximately 1950, that is, from Serre's celebrated “singular homologies of fiber spaces.”