Author: Publisher:
ISBN:
Category :
Languages : en
Pages : 63
Book Description
Geometric Classification of Simplicial Structures on Topological Manifolds
Author: Geometrical Classification of Simplicial Structures on Topological Manifolds
Author: Metod AlifSimplicial Structures in Topology
Author: Davide L. FerrarioPublisher: Springer Science & Business Media
ISBN: 1441972366
Category : Mathematics
Languages : en
Pages : 254
Book Description
Simplicial Structures in Topology provides a clear and comprehensive introduction to the subject. Ideas are developed in the first four chapters. The fifth chapter studies closed surfaces and gives their classification. The last chapter of the book is devoted to homotopy groups, which are used in short introduction on obstruction theory. The text is more in tune with the original development of algebraic topology as given by Henry Poincaré (singular homology is discussed). Illustrative examples throughout and extensive exercises at the end of each chapter for practice enhance the text. Advanced undergraduate and beginning graduate students will benefit from this book. Researchers and professionals interested in topology and applications of mathematics will also find this book useful.
Geometric Classifiction of Simplicial Structures on Topological Manifolds
Author: Metod AlifPublisher:
ISBN:
Category : Manifolds (Mathematics)
Languages : en
Pages : 63
Book Description
Piecewise Linear Structures On Topological Manifolds
Author: Yuli RudyakPublisher: World Scientific
ISBN: 9814733806
Category : Mathematics
Languages : en
Pages : 129
Book Description
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.
Algebraic and Geometric Topology, Part 2
Author: R. James MilgramPublisher: American Mathematical Soc.
ISBN: 0821814338
Category : Mathematics
Languages : en
Pages : 330
Book Description
Contains sections on Structure of topological manifolds, Low dimensional manifolds, Geometry of differential manifolds and algebraic varieties, $H$-spaces, loop spaces and $CW$ complexes, Problems.
Foundational Essays on Topological Manifolds, Smoothings, and Triangulations. (AM-88), Volume 88
Author: Robion C. KirbyPublisher: Princeton University Press
ISBN: 1400881501
Category : Mathematics
Languages : en
Pages : 368
Book Description
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.
Algorithmic Topology and Classification of 3-Manifolds
Author: Sergei MatveevPublisher: Springer Science & Business Media
ISBN: 3662051028
Category : Mathematics
Languages : en
Pages : 487
Book Description
Here is a thorough review of topics in 3-dimensional topology, derived from a decade of courses taught by the author. The author keeps the exposition to an elementary level by presenting the material mainly from the point of view of special polyhedra and special spines of 3-manifolds. The book culminates with the recognition procedure for Haken manifolds, and includes up-to-date results in computer enumeration of 3-mainfolds. The second edition adds new results, new proofs, and commentaries. Algorithmic Topology and Classification of 3-Manifolds serves as a standard reference for algorithmic 3-dimensional topology for both graduate students and researchers.
Geometric and Topological Inference
Author: Jean-Daniel BoissonnatPublisher: Cambridge University Press
ISBN: 1108419399
Category : Computers
Languages : en
Pages : 247
Book Description
A rigorous introduction to geometric and topological inference, for anyone interested in a geometric approach to data science.
Introduction to Topological Manifolds
Author: John LeePublisher: Springer Science & Business Media
ISBN: 1441979409
Category : Mathematics
Languages : en
Pages : 446
Book Description
This book is an introduction to manifolds at the beginning graduate level, and accessible to any student who has completed a solid undergraduate degree in mathematics. It contains the essential topological ideas that are needed for the further study of manifolds, particularly in the context of differential geometry, algebraic topology, and related fields. Although this second edition has the same basic structure as the first edition, it has been extensively revised and clarified; not a single page has been left untouched. The major changes include a new introduction to CW complexes (replacing most of the material on simplicial complexes in Chapter 5); expanded treatments of manifolds with boundary, local compactness, group actions, and proper maps; and a new section on paracompactness.