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Decompositions of Manifolds
Author:
Publisher: Academic Press
Published: 1986-12-22
Total Pages: 316
ISBN-13: 9780080874432
DOWNLOAD EBOOK →Decompositions of Manifolds
Cellular Decompositions of 3-Manifolds that Yield 3-Manifolds
Author: Steve Armentrout
Publisher: American Mathematical Soc.
Published: 1971
Total Pages: 76
ISBN-13: 0821818074
DOWNLOAD EBOOK →Decompositions of Manifolds
Author: Robert J. Daverman
Publisher: American Mathematical Soc.
Published: 2007
Total Pages: 317
ISBN-13: 9780821843727
DOWNLOAD EBOOK →Decomposition theory studies decompositions, or partitions, of manifolds into simple pieces, usually cell-like sets. Since its inception in 1929, the subject has become an important tool in geometric topology. The main goal of the book is to help students interested in geometric topology to bridge the gap between entry-level graduate courses and research at the frontier as well as to demonstrate interrelations of decomposition theory with other parts of geometric topology. With numerous exercises and problems, many of them quite challenging, the book continues to be strongly recommended to everyone who is interested in this subject. The book also contains an extensive bibliography and a useful index of key words, so it can also serve as a reference to a specialist.
Decompositions of Three-manifolds Into Toroidal Continua
Geometric Topology and Shape Theory
Author: Sibe Mardesic
Publisher: Springer
Published: 2006-11-14
Total Pages: 266
ISBN-13: 3540479759
DOWNLOAD EBOOK →The aim of this international conference the third of its type was to survey recent developments in Geometric Topology and Shape Theory with an emphasis on their interaction. The volume contains original research papers and carefully selected survey of currently active areas. The main topics and themes represented by the papers of this volume include decomposition theory, cell-like mappings and CE-equivalent compacta, covering dimension versus cohomological dimension, ANR's and LCn-compacta, homology manifolds, embeddings of continua into manifolds, complement theorems in shape theory, approximate fibrations and shape fibrations, fibered shape, exact homologies and strong shape theory.
Inverse Limits
Author: W.T. Ingram
Publisher: Springer Science & Business Media
Published: 2011-11-06
Total Pages: 229
ISBN-13: 146141797X
DOWNLOAD EBOOK →Inverse limits provide a powerful tool for constructing complicated spaces from simple ones. They also turn the study of a dynamical system consisting of a space and a self-map into a study of a (likely more complicated) space and a self-homeomorphism. In four chapters along with an appendix containing background material the authors develop the theory of inverse limits. The book begins with an introduction through inverse limits on [0,1] before moving to a general treatment of the subject. Special topics in continuum theory complete the book. Although it is not a book on dynamics, the influence of dynamics can be seen throughout; for instance, it includes studies of inverse limits with maps from families of maps that are of interest to dynamicists such as the logistic and the tent families. This book will serve as a useful reference to graduate students and researchers in continuum theory and dynamical systems. Researchers working in applied areas who are discovering inverse limits in their work will also benefit from this book.
Topics on Continua
Author: Sergio Macias
Publisher: CRC Press
Published: 2005-05-26
Total Pages: 374
ISBN-13: 1420026534
DOWNLOAD EBOOK →Specialized as it might be, continuum theory is one of the most intriguing areas in mathematics. However, despite being popular journal fare, few books have thoroughly explored this interesting aspect of topology. In Topics on Continua, Sergio Macias, one of the field's leading scholars, presents four of his favorite continuum topics: inv
Topics on Continua
Author: Sergio Macías
Publisher: Springer
Published: 2018-07-24
Total Pages: 441
ISBN-13: 3319909029
DOWNLOAD EBOOK →This book is a significant companion text to the existing literature on continuum theory. It opens with background information of continuum theory, so often missing from the preceding publications, and then explores the following topics: inverse limits, the Jones set function T, homogenous continua, and n-fold hyperspaces. In this new edition of the book, the author builds on the aforementioned topics, including the unprecedented presentation of n-fold hyperspace suspensions and induced maps on n-fold hyperspaces. The first edition of the book has had a remarkable impact on the continuum theory community. After twelve years, this updated version will also prove to be an excellent resource within the field of topology.
Set Function T
Author: Sergio Macías
Publisher: Springer Nature
Published: 2021-04-20
Total Pages: 225
ISBN-13: 3030650812
DOWNLOAD EBOOK →This book presents, in a clear and structured way, the set function \mathcal{T} and how it evolved since its inception by Professor F. Burton Jones in the 1940s. It starts with a very solid introductory chapter, with all the prerequisite material for navigating through the rest of the book. It then gradually advances towards the main properties, Decomposition theorems, \mathcal{T}-closed sets, continuity and images, to modern applications. The set function \mathcal{T} has been used by many mathematicians as a tool to prove results about the semigroup structure of the continua, and about the existence of a metric continuum that cannot be mapped onto its cone or to characterize spheres. Nowadays, it has been used by topologists worldwide to investigate open problems in continuum theory. This book can be of interest to both advanced undergraduate and graduate students, and to experienced researchers as well. Its well-defined structure make this book suitable not only for self-study but also as support material to seminars on the subject. Its many open problems can potentially encourage mathematicians to contribute with further advancements in the field.
