Moduli Spaces Of Riemannian Metrics PDF Download
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Author | : Wilderich Tuschmann |
Publisher | : Springer |
Total Pages | : 127 |
Release | : 2015-10-14 |
Genre | : Mathematics |
ISBN | : 3034809484 |
Download Moduli Spaces of Riemannian Metrics Book in PDF, ePub and Kindle
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.
Author | : Lutz Habermann |
Publisher | : Springer |
Total Pages | : 123 |
Release | : 2007-05-06 |
Genre | : Mathematics |
ISBN | : 3540444432 |
Download Riemannian Metrics of Constant Mass and Moduli Spaces of Conformal Structures Book in PDF, ePub and Kindle
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.
Author | : Jan-Bernhard Kordaß |
Publisher | : |
Total Pages | : 134 |
Release | : 2018 |
Genre | : |
ISBN | : |
Download On Spaces and Moduli Spaces of Riemannian Metrics Satisfying Curvature Conditions Book in PDF, ePub and Kindle
Author | : David Degen |
Publisher | : |
Total Pages | : 0 |
Release | : 2023 |
Genre | : |
ISBN | : |
Download On the Global Topology of Moduli Spaces of Riemannian Metrics with Holonomy $\operatorname˜Sp}(n)$œ Book in PDF, ePub and Kindle
Author | : David Degen |
Publisher | : |
Total Pages | : 0 |
Release | : 2022* |
Genre | : |
ISBN | : |
Download On the Global Topology of Moduli Spaces of Riemannian Metrics with Holonomy Sp(n) Book in PDF, ePub and Kindle
Author | : Benson Farb |
Publisher | : American Mathematical Soc. |
Total Pages | : 371 |
Release | : 2013-08-16 |
Genre | : Mathematics |
ISBN | : 0821898876 |
Download Moduli Spaces of Riemann Surfaces Book in PDF, ePub and Kindle
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.
Author | : Shmuel Weinberger |
Publisher | : Princeton University Press |
Total Pages | : 204 |
Release | : 2005 |
Genre | : Computers |
ISBN | : 9780691118895 |
Download Computers, Rigidity, and Moduli Book in PDF, ePub and Kindle
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.
Author | : Ana Karla García Pérez |
Publisher | : |
Total Pages | : |
Release | : 2020 |
Genre | : |
ISBN | : |
Download Spaces and Moduli Spaces of Flat Riemannian Metrics on Closed Manifolds Book in PDF, ePub and Kindle
Author | : Shmuel Weinberger |
Publisher | : Princeton University Press |
Total Pages | : 190 |
Release | : 2020-12-08 |
Genre | : Mathematics |
ISBN | : 0691222460 |
Download Computers, Rigidity, and Moduli Book in PDF, ePub and Kindle
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.
Author | : Clifford Taubes |
Publisher | : American Mathematical Soc. |
Total Pages | : 98 |
Release | : 1996 |
Genre | : Mathematics |
ISBN | : 0821803239 |
Download Metrics, Connections and Gluing Theorems Book in PDF, ePub and Kindle
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.