Описание: A number of important results in combinatorics, discrete geometry, and theoretical computer science have been proved using algebraic topology. While the results are quite famous, their proofs are not so widely understood. They are scattered in research papers or outlined in surveys, and they often use topological notions not commonly known among combinatorialists or computer scientists.This book is the first textbook treatment of a significant part of such results. It focuses on so-called equivariant methods, based on the Borsuk-Ulam theorem and its generalizations. The topological tools are intentionally kept on a very elementary level (for example, homology theory and homotopy groups are completely avoided). No prior knowledge of algebraic topology is assumed, only a background in undergraduate mathematics, and the required topological notions and results are gradually explained. This text started with a one-semester graduate course the author taught in fall 1993 in Prague. The transcripts of the lectures by the participants served as a basis of the first version. Some years later, a course partially based on that text was taught by GГјnter M. Ziegler in Berlin. The book is based on a thoroughly rewritten version prepared during a pre-doctoral course the author taught at the ETH Zurich in fall 2001.Most of the material was covered in the course: Chapter 1 was assigned as an introductory reading text, and the other chapters were presented in approximately 30 hours of teaching (by 45 minutes), with some omissions throughout and with only a sketchy presentation of the last chapter.
Автор: Milnor John Название: Lectures on the H-Cobordism Theorem ISBN: 0691624550 ISBN-13(EAN): 9780691624556 Издательство: Wiley Рейтинг: Цена: 4752.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: These lectures provide students and specialists with preliminary and valuable information from university courses and seminars in mathematics. This set gives new proof of the h-cobordism theorem that is different from the original proof presented by S. Smale. Originally published in 1965. The Princeton Legacy Library uses the latest print-on-dema
Автор: Marc Levine; Fabien Morel Название: Algebraic Cobordism ISBN: 3642071910 ISBN-13(EAN): 9783642071911 Издательство: Springer Рейтинг: Цена: 11878.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: Following Quillen`s approach to complex cobordism, the authors introduce the notion of oriented cohomology theory on the category of smooth varieties over a fixed field. They prove the existence of a universal such theory (in characteristic 0) called Algebraic Cobordism. The book also contains some examples of computations and applications.
Автор: Stong Robert E. Название: Notes on Cobordism Theory ISBN: 0691622213 ISBN-13(EAN): 9780691622217 Издательство: Wiley Рейтинг: Цена: 11088.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: These notes contain the first complete treatment of cobordism, a topic that has become increasingly important in the past ten years. The subject is fully developed and the latest theories are treated. Originally published in 1968. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-pri
Автор: Stong Robert E. Название: Notes on Cobordism Theory ISBN: 0691649014 ISBN-13(EAN): 9780691649016 Издательство: Wiley Рейтинг: Цена: 31350.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: These notes contain the first complete treatment of cobordism, a topic that has become increasingly important in the past ten years. The subject is fully developed and the latest theories are treated. Originally published in 1968. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-pri
Автор: Yu. B. Rudyak Название: On Thom Spectra, Orientability, and Cobordism ISBN: 3642082831 ISBN-13(EAN): 9783642082832 Издательство: Springer Рейтинг: Цена: 24456.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание:
For many years, algebraic topology rests on three legs: "ordinary" cohomology, K-theory, and cobordism. This book is the first guide on the subject of cobordism since R. Stong's encyclopaedic and influential notes of a generation ago. It concentrates on Thom spaces (spectra), orientability theory and (co)bordism theory (including (co)bordism with singularities and, in particular, Morava K-theories), framed by (co)homology theories and spectra.
From the Foreword by Haynes Miller
The author has also performed a service to the history of science in this book, giving detailed attributions. This same care makes the book easy to use by the student, for when proofs are not given, specific references are.
From the reviews:
..". This is an important, formidable monograph ..... The readers interested in pursuing this line of research will find it enormously helpful to have the results assembled in one place with an unified, brilliant exposition."
Zentralblatt Math 906.1999
"This book provides an excellent and thorough treatment of various topics related to cobordism. It should become an indispensable tool for advanced graduate students and workers in algebraic topology. ..."
MathSciNet MR1627486
Автор: Christoph Hummel Название: Gromov`s Compactness Theorem for Pseudo-holomorphic Curves ISBN: 3034898428 ISBN-13(EAN): 9783034898423 Издательство: Springer Рейтинг: Цена: 6986.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: This book presents the original proof of Gromov`s compactness theorem for pseudo-holomorphic curves in detail. Local properties of pseudo-holomorphic curves are investigated and proved from a geometric viewpoint.
Автор: Wen-ts?n Wu; X. Jin; D. Wang Название: Mechanical Theorem Proving in Geometries ISBN: 3211825061 ISBN-13(EAN): 9783211825068 Издательство: Springer Рейтинг: Цена: 12157.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: " Dur- ing the time of the ancient Greeks, there were two different methods dealing with geometry: one, represented by the Euclid`s "Elements," purely pursued the logical relations among geometric entities, excluding completely the quantita- tive relations, as to establish the axiom system of geometry.
Автор: Haesemeyer Christian, Weibel Charles A. Название: The Norm Residue Theorem in Motivic Cohomology ISBN: 0691191042 ISBN-13(EAN): 9780691191041 Издательство: Wiley Рейтинг: Цена: 11880.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание:
This book presents the complete proof of the Bloch-Kato conjecture and several related conjectures of Beilinson and Lichtenbaum in algebraic geometry. Brought together here for the first time, these conjectures describe the structure of tale cohomology and its relation to motivic cohomology and Chow groups.
Although the proof relies on the work of several people, it is credited primarily to Vladimir Voevodsky. The authors draw on a multitude of published and unpublished sources to explain the large-scale structure of Voevodsky's proof and introduce the key figures behind its development. They proceed to describe the highly innovative geometric constructions of Markus Rost, including the construction of norm varieties, which play a crucial role in the proof. The book then addresses symmetric powers of motives and motivic cohomology operations.
Comprehensive and self-contained, The Norm Residue Theorem in Motivic Cohomology unites various components of the proof that until now were scattered across many sources of varying accessibility, often with differing hypotheses, definitions, and language.
Описание: This book is the ninth volume in a series whose goal is to furnish a careful and largely self-contained proof of the classification theorem for the finite simple groups. Having completed the classification of the simple groups of odd type as well as the classification of the simple groups of generic even type (modulo uniqueness theorems to appear later), the current volume begins the classification of the finite simple groups of special even type. The principal result of this volume is a classification of the groups of bicharacteristic type, i.e., of both even type and of $p$-type for a suitable odd prime $p$. It is here that the largest sporadic groups emerge, namely the Monster, the Baby Monster, the largest Conway group, and the three Fischer groups, along with six finite groups of Lie type over small fields, several of which play a major role as subgroups or sections of these sporadic groups.
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