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Moduli spaces of riemannian metrics

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...

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Detalles Bibliográficos
Autores principales: Tuschmann, Wilderich, Wraith, David J
Lenguaje:eng
Publicado: Springer 2015
Materias:
Acceso en línea:https://dx.doi.org/10.1007/978-3-0348-0948-1
http://cds.cern.ch/record/2146576
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author Tuschmann, Wilderich
Wraith, David J
author_facet Tuschmann, Wilderich
Wraith, David J
author_sort Tuschmann, Wilderich
collection CERN
description 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.
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spelling cern-21465762021-04-21T19:43:25Zdoi:10.1007/978-3-0348-0948-1http://cds.cern.ch/record/2146576engTuschmann, WilderichWraith, David JModuli spaces of riemannian metricsMathematical Physics and MathematicsThis 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.Springeroai:cds.cern.ch:21465762015
spellingShingle Mathematical Physics and Mathematics
Tuschmann, Wilderich
Wraith, David J
Moduli spaces of riemannian metrics
title Moduli spaces of riemannian metrics
title_full Moduli spaces of riemannian metrics
title_fullStr Moduli spaces of riemannian metrics
title_full_unstemmed Moduli spaces of riemannian metrics
title_short Moduli spaces of riemannian metrics
title_sort moduli spaces of riemannian metrics
topic Mathematical Physics and Mathematics
url https://dx.doi.org/10.1007/978-3-0348-0948-1
http://cds.cern.ch/record/2146576
work_keys_str_mv AT tuschmannwilderich modulispacesofriemannianmetrics
AT wraithdavidj modulispacesofriemannianmetrics