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Author: John W. Morgan Publisher: American Mathematical Soc. ISBN: 9780821843284 Category : Poincaré conjecture Languages : en Pages : 586
Book Description
For over 100 years the Poincare Conjecture, which proposes a topological characterization of the 3-sphere, has been the central question in topology. Since its formulation, it has been repeatedly attacked, without success, using various topological methods. Its importance and difficulty were highlighted when it was chosen as one of the Clay Mathematics Institute's seven Millennium Prize Problems. in 2002 and 2003 Grigory Perelman posted three preprints showing how to use geometric arguments, in particular the Ricci flow as introduced and studied by Hamilton, to establish the Poincare Conjecture in the affirmative. This book provides full details of a complete proof of the Poincare Conjecture following Perelman's three preprints. After a lengthy introduction that outlines the entire argument, the book is divided into four parts. The first part reviews necessary results from Riemannian geometry and Ricci flow, including much of Hamilton's work. The second part starts with Perelman's length function, which is used to establish crucial non-collapsing theorems. Then it discusses the classification of non-collapsed, ancient solutions to the Ricci flow equation. The third part concerns the existence of Ricci flow with surgery for all positive time and an analysis of the topological and geometric changes introduced by surgery. The last part follows Perelman's third preprint to prove that when the initial Riemannian 3-manifold has finite fundamental group, Ricci flow with surgery becomes extinct after finite time. The proofs of the Poincare Conjecture and the closely related 3-dimensional spherical space-form conjectu The existence of Ricci flow with surgery has application to 3-manifolds far beyond the Poincare Conjecture. It forms the heart of the proof via Ricci flow of Thurston's Geometrization Conjecture. Thurston's Geometrization Conjecture, which classifies all compact 3-manifolds, will be the subject of a follow-up article. The organization of the material in this book differs from that given by Perelman. From the beginning the authors present all analytic and geometric arguments in the context of Ricci flow with surgery. in addition, the fourth part is a much-expanded version of Perelman's third preprint; it gives the first complete and detailed proof of the finite-time extinction theorem. With the large amount of background material that is presented and the detailed versions of the central arguments, this book is suitable for all mathematicians from advanced graduate students to specialists in geometry and topology. Clay Mathematics Institute Monograph Series The Clay Mathematics Institute Monograph Series publishes selected expositions of recent developments, both in emerging areas and in older subjects transformed by new insights or unifying ideas. Information for our distributors: Titles in this series are co-published with the Clay Mathematics Institute (Cambridge, MA).
Author: John W. Morgan Publisher: American Mathematical Soc. ISBN: 9780821843284 Category : Poincaré conjecture Languages : en Pages : 586
Book Description
For over 100 years the Poincare Conjecture, which proposes a topological characterization of the 3-sphere, has been the central question in topology. Since its formulation, it has been repeatedly attacked, without success, using various topological methods. Its importance and difficulty were highlighted when it was chosen as one of the Clay Mathematics Institute's seven Millennium Prize Problems. in 2002 and 2003 Grigory Perelman posted three preprints showing how to use geometric arguments, in particular the Ricci flow as introduced and studied by Hamilton, to establish the Poincare Conjecture in the affirmative. This book provides full details of a complete proof of the Poincare Conjecture following Perelman's three preprints. After a lengthy introduction that outlines the entire argument, the book is divided into four parts. The first part reviews necessary results from Riemannian geometry and Ricci flow, including much of Hamilton's work. The second part starts with Perelman's length function, which is used to establish crucial non-collapsing theorems. Then it discusses the classification of non-collapsed, ancient solutions to the Ricci flow equation. The third part concerns the existence of Ricci flow with surgery for all positive time and an analysis of the topological and geometric changes introduced by surgery. The last part follows Perelman's third preprint to prove that when the initial Riemannian 3-manifold has finite fundamental group, Ricci flow with surgery becomes extinct after finite time. The proofs of the Poincare Conjecture and the closely related 3-dimensional spherical space-form conjectu The existence of Ricci flow with surgery has application to 3-manifolds far beyond the Poincare Conjecture. It forms the heart of the proof via Ricci flow of Thurston's Geometrization Conjecture. Thurston's Geometrization Conjecture, which classifies all compact 3-manifolds, will be the subject of a follow-up article. The organization of the material in this book differs from that given by Perelman. From the beginning the authors present all analytic and geometric arguments in the context of Ricci flow with surgery. in addition, the fourth part is a much-expanded version of Perelman's third preprint; it gives the first complete and detailed proof of the finite-time extinction theorem. With the large amount of background material that is presented and the detailed versions of the central arguments, this book is suitable for all mathematicians from advanced graduate students to specialists in geometry and topology. Clay Mathematics Institute Monograph Series The Clay Mathematics Institute Monograph Series publishes selected expositions of recent developments, both in emerging areas and in older subjects transformed by new insights or unifying ideas. Information for our distributors: Titles in this series are co-published with the Clay Mathematics Institute (Cambridge, MA).
Author: Moira Stewart Publisher: Radcliffe Publishing ISBN: 9781857759815 Category : Medical Languages : en Pages : 380
Book Description
Divided into four parts, this volume comprehensively covers the evolution of patient-centered care, the six interactive components of the patient-centered clinical method, teaching and learning, and research including findings and reviews. It explains the basis and development of the clinical method.
Author: Ihsan Boustani Publisher: Springer Nature ISBN: 3030327264 Category : Technology & Engineering Languages : en Pages : 594
Book Description
This book presents nanomaterials as predicted by computational modelling and numerical simulation tools, and confirmed by modern experimental techniques. It begins by summarizing basic theoretical methods, then giving both a theoretical and experimental treatment of how alkali metal clusters develop into nanostructures, as influenced by the cluster's "magic number" of atoms. The book continues with a discussion of atomic clusters and nanostructures, focusing primarily on boron and carbon, exploring, in detail, the one-, two-, and three-dimensional structures of boron and carbon, and describing their myriad potential applications in nanotechnology, from nanocoating and nanosensing to nanobatteries with high borophene capacity. The broad discussion of computational modelling as well as the specific applications to boron and carbon, make this book an essential reference resource for materials scientists in this field of research.
Author: Ruth W. Chabay Publisher: John Wiley & Sons ISBN: 0470503475 Category : Science Languages : en Pages : 1128
Book Description
Matter and Interactions offers a modern curriculum for introductory physics (calculus-based). It presents physics the way practicing physicists view their discipline and integrates 20th Century physics and computational physics. The text emphasizes the small number of fundamental principles that underlie the behavior of matter, and models that can explain and predict a wide variety of physical phenomena. Matter and Interactions will be available as a single volume hardcover text and also two paperback volumes.
Author: F. Albert Cotton Publisher: John Wiley & Sons ISBN: 0471505323 Category : Science Languages : en Pages : 858
Book Description
Explains the basics of inorganic chemistry with a primary emphasis on facts; then uses the student's growing factual knowledge as a foundation for discussing the important principles of periodicity in structure, bonding and reactivity. New to this updated edition: improved treatment of atomic orbitals and properties such as electronegativity, novel approaches to the depiction of ionic structures, nomenclature for transition metal compounds, quantitative approaches to acid-base chemistry, Wade's rules for boranes and carboranes, the chemistry of major new classes of substances including fullerenes and silenes plus a chapter on the inorganic solid state.
Author: Soshin Chikazumi Publisher: Oxford University Press, USA ISBN: 0199564817 Category : Science Languages : en Pages : 669
Book Description
This book is a textbook for graduate students and researchers who are interested in ferromagnetism. The emphasis is primarily on explanation of physical concepts rather than on a rigorous theoretical treatment.
Author: W. Andreoni Publisher: Springer Science & Business Media ISBN: 9780792362340 Category : Science Languages : en Pages : 474
Book Description
Krätschmer and Huffman's revolutionary discovery of a new solid phase of carbon, solid C60, in 1990 opened the way to an entire new class of materials with physical properties so diverse that their richness has not yet been fully exploited. Moreover, as a by-product of fullerene research, carbon nanotubes were later identified, from which novel nanostructures originated that are currently fascinating materials scientists worldwide. Rivers of words have been written on both fullerenes and nanotubes, in the form of journal articles, conference proceedings and books. The present book offers, in a concise and self-contained manner, the basics of the science of these materials as well as detailed information on those aspects that have so far been better explored. Structural, electronic and dynamical properties are described as obtained from various measurements and state-of-the-art calculations. Their interrelation emerges as well as their possible dependence on, for example, preparation conditions or methods of investigation. By presenting and comparing data from different sources, experiment and theory, this book helps the reader to rapidly master the basic knowledge, to grasp important issues and critically discuss them. Ultimately, it aims to inspire him or her to find novel ways to approach still open questions. As such, this book is addressed to new researchers in the field as well as experts.
Author: Donald Voet Publisher: John Wiley & Sons ISBN: 1119770645 Category : Biochemistry Languages : en Pages : 1490
Book Description
The "Gold Standard" in Biochemistry text books. Biochemistry 4e, is a modern classic that has been thoroughly revised. Don and Judy Voet explain biochemical concepts while offering a unified presentation of life and its variation through evolution. It incorporates both classical and current research to illustrate the historical source of much of our biochemical knowledge.
Author: Mahmoud Filali Publisher: Walter de Gruyter GmbH & Co KG ISBN: 3110600439 Category : Mathematics Languages : en Pages : 264
Book Description
Banach algebras is a multilayered area in mathematics with many ramifications. With a diverse coverage of different schools working on the subject, this proceedings volume reflects recent achievements in areas such as Banach algebras over groups, abstract harmonic analysis, group actions, amenability, topological homology, Arens irregularity, C*-algebras and dynamical systems, operator theory, operator spaces, and locally compact quantum groups.