Moduli Spaces of Riemannian Metrics

David J. Wraith

ISBN 10: 3034809476 / ISBN 13: 9783034809474

Verlag: Springer Basel, Springer Basel Okt 2015, 2015

Beschreibung

Neuware -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.Springer Basel AG in Springer Science + Business Media, Heidelberger Platz 3, 14197 Berlin 136 pp. Englisch.

Bestandsnummer des Verkäufers 9783034809474

Bibliografische Details

• Titel: Moduli Spaces of Riemannian Metrics
• Verlag: Springer Basel, Springer Basel Okt 2015
• Erscheinungsjahr: 2015
• Sprache: Englisch
• ISBN-10: 3034809476
• ISBN-13: 9783034809474
• Einband: Taschenbuch
• Zustand: Neu

Über diesen Titel

Inhaltsangabe

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.

Über die Autorin bzw. den Autor

Wilderich Tuschmann's general research interests lie in the realms of global differential geometry, Riemannian geometry, geometric topology, and their applications, including, for example, questions concerning the geometry and topology of nonnegative and almost nonnegative curvature, singular metric spaces, collapsing and Gromov-Hausdorff convergence, analysis and geometry on Alexandrov spaces, geometric finiteness theorems, moduli spaces of Riemannian metrics, transformation groups, geometric bordism invariants, information and quantum information geometry. After his habilitation in mathematics at the University of Leipzig in 2000 he worked as a Deutsche Forschungsgemeinschaft Heisenberg Fellow at Westfälische Wilhems-Universität Münster, and from 2005-2010 he held a professorship at Christian-Albrechts-Universität Kiel. In the fall of 2010 he was appointed professor of mathematics at Karlsruhe Institute of Technology (KIT), a position he currently holds. David Wraith's main mathematical interests concern the existence of Riemannian metrics satisfying various kinds of curvature conditions and their topological implications. Most of his work to date has focused on the existence of positive Ricci curvature metrics. He has worked at the National University of Ireland Maynooth since 1997.