Ricci Flow and the Poincare Conjecture PDF Download

Are you looking for read ebook online? Search for your book and save it on your Kindle device, PC, phones or tablets. Download Ricci Flow and the Poincare Conjecture PDF full book. Access full book title Ricci Flow and the Poincare Conjecture by John W. Morgan. Download full books in PDF and EPUB format.

Ricci Flow and the Poincare Conjecture

Ricci Flow and the Poincare Conjecture PDF Author: John W. Morgan
Publisher: American Mathematical Soc.
ISBN: 9780821843284
Category : Mathematics
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).

Ricci Flow and the Poincare Conjecture

Ricci Flow and the Poincare Conjecture PDF Author: John W. Morgan
Publisher: American Mathematical Soc.
ISBN: 9780821843284
Category : Mathematics
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).

Molecular Modelling and Synthesis of Nanomaterials

Molecular Modelling and Synthesis of Nanomaterials PDF Author: Ihsan Boustani
Publisher: Springer Nature
ISBN: 3030327264
Category : Technology & Engineering
Languages : en
Pages : 598

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.

Energy Research Abstracts

Energy Research Abstracts PDF Author:
Publisher:
ISBN:
Category : Power resources
Languages : en
Pages : 770

Book Description


Basic Inorganic Chemistry

Basic Inorganic Chemistry PDF 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.

NASA Technical Paper

NASA Technical Paper PDF Author:
Publisher:
ISBN:
Category : Science
Languages : en
Pages : 36

Book Description


CONCISE ORGANIC CHEMISTRY

CONCISE ORGANIC CHEMISTRY PDF Author: Dr. Kamlodvab Jha
Publisher: Booksclinic Publishing
ISBN: 9358238631
Category : Education
Languages : en
Pages : 280

Book Description
The book has been written for those students who wish to pursue B.Sc.chemistry Honours or general courses by covering the syllabuses of all the Indian Universities. The book is also suitable for the students who is preparing the JAM entrance examinations for M.Sc. courses. The book has been written in very simple language with clear three dimensional diagrams and appropriate reaction mechanism. It contains many problems which will useful for the readers.

The Chemistry of Diamondoids

The Chemistry of Diamondoids PDF Author: Andrey A. Fokin
Publisher: John Wiley & Sons
ISBN: 3527812938
Category : Technology & Engineering
Languages : en
Pages : 373

Book Description
The Chemistry of Diamondoids Comprehensive resource on an important and fascinating compound class, covering synthesis, properties, functionalization, and applications in organic synthesis, materials science, and more The Chemistry of Diamondoids gives a state-of-the-art overview of all aspects of diamondoid chemistry, covering nomenclature, natural occurrence, chemical and physical properties, along with synthesis and functionalization of diamondoids as well as their applications as molecular building blocks in organic synthesis, polymer and materials science, nanotechnology, and medicinal chemistry. The book concludes with a perspective towards future developments in the field, thereby drawing attention to areas open for discovery. Written by experts in the field, The Chemistry of Diamondoids includes information on: Naturally occurring diamondoids, their formation, and the role they play in the petroleum industry and in geosciences, plus man-made approaches to prepare them on large scale Growing diamond from diamondoids via seeding, preparation and properties of diamondoid oligomers and doped diamondoids C–H-bond functionalization, a precondition for their use in many applications, and fine-tuning of diamondoid properties by precise cage substitution reactions With its all-encompassing approach, The Chemistry of Diamondoids is a valuable guide for newcomers and researchers in organic chemistry and materials science interested in modern synthetic methods and organic functional materials.

Structural Chemistry across the Periodic Table

Structural Chemistry across the Periodic Table PDF Author: Thomas CW Mak
Publisher: Oxford University Press
ISBN: 0198872968
Category : Science
Languages : en
Pages : 593

Book Description
This book is an expanded and updated version of Part III of the authors' previous work, Advanced Structural Inorganic Chemistry (OUP 2008). The original part deals with main-group elements, the rare-earth elements, transition-metal clusters, and supramolecular systems. In this new book, selected material from significant advances in the past decade has been added, with particular emphasis on compounds that exemplify new types of bonds such as sigma-hole, triel bond, tetrel bond, pnictogen bond, chalcogen bond, halogen bond, halogen-halogen interaction, aerogen bond, as well as quintuple and sextuple metal-metal bonds. Other new topics include actinide compounds, metallophilicity, heterometallic macrocycles and cages, com- and dis-proportionation reactions, hydrogen-bonded organic frameworks (HOFs), halogen-bonded organic frameworks, halogen-halogen interactions in supramolecular frameworks, covalent organic frameworks (COFs), and metal-organic frameworks (MOFs).

Principles of Inorganic Chemistry

Principles of Inorganic Chemistry PDF Author: Brian W. Pfennig
Publisher: John Wiley & Sons
ISBN: 111965033X
Category : Science
Languages : en
Pages : 836

Book Description
PRINCIPLES OF INORGANIC CHEMISTRY Discover the foundational principles of inorganic chemistry with this intuitively organized new edition of a celebrated textbook In the newly revised Second Edition of Principles of Inorganic Chemistry, experienced researcher and chemist Dr. Brian W. Pfennig delivers an accessible and engaging exploration of inorganic chemistry perfect for sophomore-level students. This redesigned book retains all of the rigor of the first edition but reorganizes it to assist readers with learning and retention. In-depth boxed sections include original mathematical derivations for more advanced students, while topics like atomic and molecular term symbols, symmetry coordinates in vibrational spectroscopy, polyatomic MO theory, band theory, and Tanabe-Sugano diagrams are all covered. Readers will find many worked examples throughout the text, as well as numerous unanswered problems at varying levels of difficulty. Informative, colorful illustrations also help to highlight and explain the concepts discussed within. The new edition includes an increased emphasis on the comparison of the strengths and weaknesses of different chemical models, the interconnectedness of valence bond theory and molecular orbital theory, as well as a more thorough discussion of the atoms in molecules topological model. Readers will also find: A thorough introduction to and treatment of group theory, with an emphasis on its applications to chemical bonding and spectroscopy A comprehensive exploration of chemical bonding that compares and contrasts the traditional classification of ionic, covalent, and metallic bonding In-depth examinations of atomic and molecular orbitals and a nuanced discussion of the interrelationship between VBT, MOT, and band theory A section on the relationship between a molecule’s structure and bonding and its chemical reactivity With its in-depth boxed discussions, this textbook is also ideal for senior undergraduate and first-year graduate students in inorganic chemistry, Principles of Inorganic Chemistry is a must-have resource for anyone seeking a principles-based approach with theoretical depth. Furthermore, it will be useful for students of physical chemistry, materials science, and chemical physics.

Advances in Photochemistry

Advances in Photochemistry PDF Author: David H. Volman
Publisher: John Wiley & Sons
ISBN: 0470133635
Category : Science
Languages : en
Pages : 494

Book Description
Setting the pace for progress and innovation . . . "[Provides] a wealth of information on frontier photochemistry . . . could easily serve as a definitive source of background information for future researchers." —Journal of the American Chemical Society "The overall quality of the series and the timeliness of selections and authors warrants continuation of the series by any library wishing to maintain a first-rate reference series to the literature." —Physics Today ADVANCES IN PHOTOCHEMISTRY More than a simple survey of the current literature, Advances in Photochemistry offers critical evaluations written by internationally recognized experts. These pioneering scientists offer unique and varied points of view of the existing data. Their articles are challenging as well as provocative and are intended to stimulate discussion, promote further research, and encourage new developments in the field.