From Calculus To Cohomology
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From Calculus To Cohomology
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Author : Ib H. Madsen
language : en
Publisher: Cambridge University Press
Release Date : 1997-03-13
From Calculus To Cohomology written by Ib H. Madsen and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997-03-13 with Mathematics categories.
An introductory textbook on cohomology and curvature with emphasis on applications.
From Calculus To Cohomology
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Author : Ib Henning Madsen
language : en
Publisher:
Release Date : 1997
From Calculus To Cohomology written by Ib Henning Madsen and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997 with Characteristic classes categories.
Cohomological Aspects In Complex Non K Hler Geometry
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Author : Daniele Angella
language : en
Publisher: Springer
Release Date : 2013-11-22
Cohomological Aspects In Complex Non K Hler Geometry written by Daniele Angella and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-11-22 with Mathematics categories.
In these notes, we provide a summary of recent results on the cohomological properties of compact complex manifolds not endowed with a Kähler structure. On the one hand, the large number of developed analytic techniques makes it possible to prove strong cohomological properties for compact Kähler manifolds. On the other, in order to further investigate any of these properties, it is natural to look for manifolds that do not have any Kähler structure. We focus in particular on studying Bott-Chern and Aeppli cohomologies of compact complex manifolds. Several results concerning the computations of Dolbeault and Bott-Chern cohomologies on nilmanifolds are summarized, allowing readers to study explicit examples. Manifolds endowed with almost-complex structures, or with other special structures (such as, for example, symplectic, generalized-complex, etc.), are also considered.
Differential Forms
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Author : Guillemin Victor
language : en
Publisher: World Scientific
Release Date : 2019-03-20
Differential Forms written by Guillemin Victor and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-03-20 with Mathematics categories.
There already exist a number of excellent graduate textbooks on the theory of differential forms as well as a handful of very good undergraduate textbooks on multivariable calculus in which this subject is briefly touched upon but not elaborated on enough.The goal of this textbook is to be readable and usable for undergraduates. It is entirely devoted to the subject of differential forms and explores a lot of its important ramifications.In particular, our book provides a detailed and lucid account of a fundamental result in the theory of differential forms which is, as a rule, not touched upon in undergraduate texts: the isomorphism between the Čech cohomology groups of a differential manifold and its de Rham cohomology groups.
Low Order Cohomology And Applications
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Author : J. Erven
language : en
Publisher:
Release Date : 2014-09-01
Low Order Cohomology And Applications written by J. Erven and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-09-01 with categories.
Differential Forms In Algebraic Topology
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Author : Raoul Bott
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-04-17
Differential Forms In Algebraic Topology written by Raoul Bott and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-04-17 with Mathematics categories.
Developed from a first-year graduate course in algebraic topology, this text 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. By using the de Rham theory of differential forms as a prototype of cohomology, the machineries of algebraic topology are made easier to assimilate. With its stress on concreteness, motivation, and readability, this book is equally suitable for self-study and as a one-semester course in topology.
An Introduction To Manifolds
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Author : Loring W. Tu
language : en
Publisher: Springer Science & Business Media
Release Date : 2010-10-05
An Introduction To Manifolds written by Loring W. Tu and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-10-05 with Mathematics categories.
Manifolds, the higher-dimensional analogs of smooth curves and surfaces, are fundamental objects in modern mathematics. Combining aspects of algebra, topology, and analysis, manifolds have also been applied to classical mechanics, general relativity, and quantum field theory. In this streamlined introduction to the subject, the theory of manifolds is presented with the aim of helping the reader achieve a rapid mastery of the essential topics. By the end of the book the reader should be able to compute, at least for simple spaces, one of the most basic topological invariants of a manifold, its de Rham cohomology. Along the way, the reader acquires the knowledge and skills necessary for further study of geometry and topology. The requisite point-set topology is included in an appendix of twenty pages; other appendices review facts from real analysis and linear algebra. Hints and solutions are provided to many of the exercises and problems. This work may be used as the text for a one-semester graduate or advanced undergraduate course, as well as by students engaged in self-study. Requiring only minimal undergraduate prerequisites, 'Introduction to Manifolds' is also an excellent foundation for Springer's GTM 82, 'Differential Forms in Algebraic Topology'.
Global Calculus
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Author : S. Ramanan
language : en
Publisher: American Mathematical Soc.
Release Date : 2005
Global Calculus written by S. Ramanan and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005 with Analytic spaces categories.
The power that analysis, topology and algebra bring to geometry has revolutionised the way geometers and physicists look at conceptual problems. Some of the key ingredients in this interplay are sheaves, cohomology, Lie groups, connections and differential operators. In Global Calculus, the appropriate formalism for these topics is laid out with numerous examples and applications by one of the experts in differential and algebraic geometry. Ramanan has chosen an uncommon but natural path through the subject. In this almost completely self-contained account, these topics are developed from scratch. The basics of Fourier transforms, Sobolev theory and interior regularity are proved at the same time as symbol calculus, culminating in beautiful results in global analysis, real and complex. Many new perspectives on traditional and modern questions of differential analysis and geometry are the hallmarks of the book. The book is suitable for a first year graduate course on Global Analysis.
Vector Analysis
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Author : Klaus Jänich
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-09
Vector Analysis written by Klaus Jänich and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-09 with Mathematics categories.
This book presents modern vector analysis and carefully describes the classical notation and understanding of the theory. It covers all of the classical vector analysis in Euclidean space, as well as on manifolds, and goes on to introduce de Rham Cohomology, Hodge theory, elementary differential geometry, and basic duality. The material is accessible to readers and students with only calculus and linear algebra as prerequisites. A large number of illustrations, exercises, and tests with answers make this book an invaluable self-study source.
Manifolds Sheaves And Cohomology
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Author : Torsten Wedhorn
language : en
Publisher: Springer
Release Date : 2016-07-25
Manifolds Sheaves And Cohomology written by Torsten Wedhorn and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-07-25 with Mathematics categories.
This book explains techniques that are essential in almost all branches of modern geometry such as algebraic geometry, complex geometry, or non-archimedian geometry. It uses the most accessible case, real and complex manifolds, as a model. The author especially emphasizes the difference between local and global questions. Cohomology theory of sheaves is introduced and its usage is illustrated by many examples.