Moduli Spaces Of Riemannian Metrics
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Moduli Spaces Of Riemannian Metrics
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Author : Wilderich Tuschmann
language : en
Publisher: Springer
Release Date : 2015-10-14
Moduli Spaces Of Riemannian Metrics written by Wilderich Tuschmann and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-10-14 with Mathematics categories.
This book studies certain spaces of Riemannian metrics on both compact and non-compact manifolds. These spaces are defined by various sign-based curvature conditions, with special attention paid to positive scalar curvature and non-negative sectional curvature, though we also consider positive Ricci and non-positive sectional curvature. If we form the quotient of such a space of metrics under the action of the diffeomorphism group (or possibly a subgroup) we obtain a moduli space. Understanding the topology of both the original space of metrics and the corresponding moduli space form the central theme of this book. For example, what can be said about the connectedness or the various homotopy groups of such spaces? We explore the major results in the area, but provide sufficient background so that a non-expert with a grounding in Riemannian geometry can access this growing area of research.
Riemannian Metrics Of Constant Mass And Moduli Spaces Of Conformal Structures
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Author : Lutz Habermann
language : en
Publisher: Springer
Release Date : 2007-05-06
Riemannian Metrics Of Constant Mass And Moduli Spaces Of Conformal Structures written by Lutz Habermann and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-05-06 with Mathematics categories.
This monograph deals with recent questions of conformal geometry. It provides in detail an approach to studying moduli spaces of conformal structures, using a new canonical metric for conformal structures. This book is accessible to readers with basic knowledge in differential geometry and global analysis. It addresses graduates and researchers.
Computers Rigidity And Moduli
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Author : Shmuel Weinberger
language : en
Publisher: Princeton University Press
Release Date : 2020-12-08
Computers Rigidity And Moduli written by Shmuel Weinberger and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-12-08 with Mathematics categories.
This book is the first to present a new area of mathematical research that combines topology, geometry, and logic. Shmuel Weinberger seeks to explain and illustrate the implications of the general principle, first emphasized by Alex Nabutovsky, that logical complexity engenders geometric complexity. He provides applications to the problem of closed geodesics, the theory of submanifolds, and the structure of the moduli space of isometry classes of Riemannian metrics with curvature bounds on a given manifold. Ultimately, geometric complexity of a moduli space forces functions defined on that space to have many critical points, and new results about the existence of extrema or equilibria follow. The main sort of algorithmic problem that arises is recognition: is the presented object equivalent to some standard one? If it is difficult to determine whether the problem is solvable, then the original object has doppelgängers--that is, other objects that are extremely difficult to distinguish from it. Many new questions emerge about the algorithmic nature of known geometric theorems, about "dichotomy problems," and about the metric entropy of moduli space. Weinberger studies them using tools from group theory, computability, differential geometry, and topology, all of which he explains before use. Since several examples are worked out, the overarching principles are set in a clear relief that goes beyond the details of any one problem.
Metrics Connections And Gluing Theorems
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Author : Clifford Taubes
language : en
Publisher: American Mathematical Soc.
Release Date : 1996
Metrics Connections And Gluing Theorems written by Clifford Taubes 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 1996 with Mathematics categories.
In this book, the author's goal is to provide an introduction to some of the analytic underpinnings for the geometry of anti-self duality in 4-dimensions. Anti-self duality is rather special to 4-dimensions and the imposition of this condition on curvatures of connections on vector bundles and on curvatures of Riemannian metrics has resulted in some spectacular mathematics. The book reviews some basic geometry, but is is assumed that the reader has a general background in differential geometry (as would be obtained by reading a standard text on the subject). Some of the fundamental references include Atiyah, Hitchin and Singer, Freed and Uhlenbeck, Donaldson and Kronheimer, and Kronheimer and Mrowka. The last chapter contains open problems and conjectures.
Metric Structures For Riemannian And Non Riemannian Spaces
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Author : Mikhail Gromov
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-06-25
Metric Structures For Riemannian And Non Riemannian Spaces written by Mikhail Gromov 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 2007-06-25 with Mathematics categories.
This book is an English translation of the famous "Green Book" by Lafontaine and Pansu (1979). It has been enriched and expanded with new material to reflect recent progress. Additionally, four appendices, by Gromov on Levy's inequality, by Pansu on "quasiconvex" domains, by Katz on systoles of Riemannian manifolds, and by Semmes overviewing analysis on metric spaces with measures, as well as an extensive bibliography and index round out this unique and beautiful book.
Contributions To And A Survey On Moduli Spaces Of Differential Geometric Structures With Applications In Physics
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Author : Osmo Pekonen
language : en
Publisher:
Release Date : 1988
Contributions To And A Survey On Moduli Spaces Of Differential Geometric Structures With Applications In Physics written by Osmo Pekonen and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1988 with Geometry, Differential categories.
Geometry And Physics
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Author : Jürgen Jost
language : en
Publisher: Springer Science & Business Media
Release Date : 2009-08-17
Geometry And Physics written by Jürgen Jost 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 2009-08-17 with Mathematics categories.
"Geometry and Physics" addresses mathematicians wanting to understand modern physics, and physicists wanting to learn geometry. It gives an introduction to modern quantum field theory and related areas of theoretical high-energy physics from the perspective of Riemannian geometry, and an introduction to modern geometry as needed and utilized in modern physics. Jürgen Jost, a well-known research mathematician and advanced textbook author, also develops important geometric concepts and methods that can be used for the structures of physics. In particular, he discusses the Lagrangians of the standard model and its supersymmetric extensions from a geometric perspective.
Geometry Of Riemann Surfaces And Teichm Ller Spaces
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Author : M. Seppälä
language : en
Publisher: Elsevier
Release Date : 2011-08-18
Geometry Of Riemann Surfaces And Teichm Ller Spaces written by M. Seppälä and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-08-18 with Mathematics categories.
The moduli problem is to describe the structure of the space of isomorphism classes of Riemann surfaces of a given topological type. This space is known as the moduli space and has been at the center of pure mathematics for more than a hundred years. In spite of its age, this field still attracts a lot of attention, the smooth compact Riemann surfaces being simply complex projective algebraic curves. Therefore the moduli space of compact Riemann surfaces is also the moduli space of complex algebraic curves. This space lies on the intersection of many fields of mathematics and may be studied from many different points of view. The aim of this monograph is to present information about the structure of the moduli space using as concrete and elementary methods as possible. This simple approach leads to a rich theory and opens a new way of treating the moduli problem, putting new life into classical methods that were used in the study of moduli problems in the 1920s.
Moduli Spaces Of Riemann Surfaces
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Author : Benson Farb
language : en
Publisher: American Mathematical Soc.
Release Date : 2013-08-16
Moduli Spaces Of Riemann Surfaces written by Benson Farb 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 2013-08-16 with Mathematics categories.
Mapping class groups and moduli spaces of Riemann surfaces were the topics of the Graduate Summer School at the 2011 IAS/Park City Mathematics Institute. This book presents the nine different lecture series comprising the summer school, covering a selection of topics of current interest. The introductory courses treat mapping class groups and Teichmüller theory. The more advanced courses cover intersection theory on moduli spaces, the dynamics of polygonal billiards and moduli spaces, the stable cohomology of mapping class groups, the structure of Torelli groups, and arithmetic mapping class groups. The courses consist of a set of intensive short lectures offered by leaders in the field, designed to introduce students to exciting, current research in mathematics. These lectures do not duplicate standard courses available elsewhere. The book should be a valuable resource for graduate students and researchers interested in the topology, geometry and dynamics of moduli spaces of Riemann surfaces and related topics. Titles in this series are co-published with the Institute for Advanced Study/Park City Mathematics Institute. Members of the Mathematical Association of America (MAA) and the National Council of Teachers of Mathematics (NCTM) receive a 20% discount from list price.
Metric Structures For Riemannian And Non Riemannian Spaces
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Author : Mikhail Gromov
language : en
Publisher: Birkhäuser
Release Date : 2008-11-01
Metric Structures For Riemannian And Non Riemannian Spaces written by Mikhail Gromov and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-11-01 with Mathematics categories.
This book is an English translation of the famous "Green Book" by Lafontaine and Pansu (1979). It has been enriched and expanded with new material to reflect recent progress. Additionally, four appendices, by Gromov on Levy's inequality, by Pansu on "quasiconvex" domains, by Katz on systoles of Riemannian manifolds, and by Semmes overviewing analysis on metric spaces with measures, as well as an extensive bibliography and index round out this unique and beautiful book.