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The Poincare Conjecture: In Search of the Shape of the Universe
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Donal O'Shea
In telling this vibrant story, O'Shea makes accessible to general readers for the first time the meaning of the conjecture, and brings alive the field of mathematics and the achievements of generations of mathematicians.
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Topology and geometry
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Bredon
This book is intended as a textbook for a first-year graduate course on algebraic topology, with as strong flavoring in smooth manifold theory. Starting with general topology, it discusses differentiable manifolds, cohomology, products and duality, the fundamental group, homology theory, and homotopy theory. It covers most of the topics all ...
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Algebraic Topology
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Allen Hatcher
In most mathematics departments at major universities one of the three or four basic first-year graduate courses is in the subject of algebraic topology. This introductory textbook in algebraic topology is suitable for use in a course or for self-study, featuring broad coverage of the subject and a readable exposition, with many examples and ...
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Lecture Notes on Elementary Topology and Geometry
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I M Singer, J a Thorpe
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Differential Forms in Algebraic Topology
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Raoul Bott, Loring W Tu
This text, developed from a first-year graduate course in algebraic topology, is an informal introduction to some of the main ideas of contemporary homotopy and cohomology theory. The materials are structured around four core areas- de Rham theory, the Cech-de Rham complex, spectral sequences, and characteristic classes-and include some ...
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A First Course in Algebraic Topology
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Czes Kosniowski
This self-contained introduction to algebraic topology is suitable for a number of topology courses. It consists of about one quarter 'general topology' (without its usual pathologies) and three quarters 'algebraic topology' (centred around the fundamental group, a readily grasped topic which gives a good idea of what algebraic topology is). The ...
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Topological Field Theory: Primitive Form and Related Topics
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Atsushi Matsuo, Kyoji Saito, Masaki Kashiwara (Editor)
As the interaction of mathematics and theoretical physics continues to intensify, the theories developed in mathematics are being applied to physics, and conversely. This book centers around the theory of primitive forms which currently plays an active and key role in topological field theory (theoretical physics), but was originally developed as ...
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Lectures on algebraic topology
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Marvin J Greenberg
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Algebraic and Differential Topology of Robust Stability
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Edmond A Jonckheere
In this book, two seemingly unrelated fields - algebraic topology and robust control - are brought together. The book develops algebraic/differential topology proceeding from an easily motivated control engineering problem, showing the relevance of advanced topological concepts and reconstructing the fundamental concepts of algebraic/differential ...
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A combinatorial introduction to topology
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Michael Henle
The creation of algebraic topology is a major accomplishment of the 20th century. The goal of this book is to show how geometric and algebraic ideas met and grew together into an important branch of mathematics in the recent past. The book also conveys the fun and adventure that can be part of a mathematical investigation.
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Algebraic Topology: An Introduction
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William S Massey
William S. Massey Professor Massey, born in Illinois in 1920, received his bachelor's degree from the University of Chicago and then served for four years in the U.S. Navy during World War II. After the War he received his Ph.D. from Princeton University and spent two additional years there as a post-doctoral research assistant. He then taught for ...
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Topology in Process Calculus: Approximate Correctness and Infinite Evolution of Concurrent Programs
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by
Mingsheng Ying
Communication and concurrency are essential in understanding complex dynamic systems, and there have been many theories to deal with them such as Petri nets, CSP and ACP. Among them, CCS (process calculus is one of the most important and mathematically developed models of communication and concurrency. Various behavior equivalences between agents, ...
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Algebraic topology
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Edwin Henry Spanier
Intended for use both as a text and a reference, this book is an exposition of the fundamental ideas of algebraic topology. The first third of the book covers the fundamental group, its definition and its application in the study of covering spaces. The focus then turns to homology theory, including cohomology, cup products, cohomology operations, ...
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Algebraic topology: homology and cohomology
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Andrew H. Wallace
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Algebraic Topology and Algebraic K-Theory: Proceedings of a Symposium in Honor of John C. Moore. (Am-113)
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William Browder (Editor), John C Moore
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Braids and Coverings: Selected Topics
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Vagn Lundsgaard Hansen
This book is based on a graduate course taught by the author at the University of Maryland, USA. The lecture notes have been revised and augmented by examples. The work falls into two strands. The first two chapters develop the elementary theory of Artin Braid groups both geometrically and via homotopy theory, and discuss the link between knot ...
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Adams Memorial Symposium on Algebraic Topology: Volume 1
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Nigel Ray (Editor), Grant Walker (Editor), N J Hitchin (Editor)
J. Frank Adams had a profound influence on algebraic topology, and his works continue to shape its development. The International Symposium on Algebraic Topology held in Manchester during July 1990 was dedicated to his memory, and virtually all of the world's leading experts took part. This two volume work constitutes the proceedings of the ...
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A Basic Course in Algebraic Topology
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William S Massey
This book is intended to serve as a textbook for a course in algebraic topology at the beginning graduate level. The main topics covered are the classification of compact 2-manifolds, the fundamental group, covering spaces, singular homology theory, and singular cohomology theory. These topics are developed systematically, avoiding all unecessary ...
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An Introduction to Algebraic Topology
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Andrew H Wallace
This self-contained treatment assumes only some knowledge of real numbers and real analysis. The first three chapters focus on the basics of point-set topology, after which the text proceeds to homology groups and continuous mapping, barycentric subdivision, and simplicial complexes. Exercises form an integral part of the text. 1961 edition.
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The algebraic characterization of geometric 4-manifolds
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Hillman
This book describes work, largely that of the author, on the characterization of closed 4-manifolds in terms of familiar invariants such as Euler characteristic, fundamental group, and Stiefel-Whitney classes. Using techniques from homological group theory, the theory of 3-manifolds and topological surgery, infrasolvmanifolds are characterized up ...
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Abstract harmonic analysis
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Edwin Hewitt, Kenneth A Ross
This book is a continuation of vol. I (Grundlehren vol. 115, also available in softcover), and contains a detailed treatment of some important parts of harmonic analysis on compact and locally compact abelian groups. From the reviews: "This work aims at giving a monographic presentation of abstract harmonic analysis, far more complete and ...
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Algebraic Topology--Homotopy and Homology
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Robert M Switzer
From the reviews:"The author has attempted an ambitious and most commendable project. He assumes only a modest knowledge of algebraic topology on the part of the reader to start with, and he leads the reader systematically to the point at which he can begin to tackle problems in the current areas of research centered around generalized homology ...
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Seminar on transformation groups
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A. Borel
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Geometric and Topological Methods for Quantum Field Theory
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Hernan Ocampo (Editor), Sylvie Paycha (Editor), Andres Vargas (Editor)
This volume offers an introduction, in the form of four extensive lectures, to some recent developments in several active topics at the interface between geometry, topology and quantum field theory. The first lecture is by Christine Lescop on knot invariants and configuration spaces, in which a universal finite-type invariant for knots is ...
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A History of Algebraic and Differential Topology, 1900-1960
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Jean Alexandre Dieudonne
A classic available again, this book traces the history of algebraic topology beginning with its creation by Henry Poincare in 1900, and describing in detail the important ideas introduced in the theory before 1960. In its first thirty years the field seemed limited to applications in algebraic geometry, but this changed dramatically in the 1930s ...
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