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The Resource Metric Structures for Riemannian and NonRiemannian Spaces, by Mikhail Gromov ; edited by Jacques LaFontaine, Pierre Pansu, (electronic resource)
Metric Structures for Riemannian and NonRiemannian Spaces, by Mikhail Gromov ; edited by Jacques LaFontaine, Pierre Pansu, (electronic resource)
Resource Information
The item Metric Structures for Riemannian and NonRiemannian Spaces, by Mikhail Gromov ; edited by Jacques LaFontaine, Pierre Pansu, (electronic resource) represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in University of Manitoba Libraries.This item is available to borrow from all library branches.
Resource Information
The item Metric Structures for Riemannian and NonRiemannian Spaces, by Mikhail Gromov ; edited by Jacques LaFontaine, Pierre Pansu, (electronic resource) represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in University of Manitoba Libraries.
This item is available to borrow from all library branches.
 Summary
 Metric theory has undergone a dramatic phase transition in the last decades when its focus moved from the foundations of real analysis to Riemannian geometry and algebraic topology, to the theory of infinite groups and probability theory. The new wave began with seminal papers by Svarc and Milnor on the growth of groups and the spectacular proof of the rigidity of lattices by Mostow. This progress was followed by the creation of the asymptotic metric theory of infinite groups by Gromov. The structural metric approach to the Riemannian category, tracing back to Cheeger's thesis, pivots around the notion of the Gromov–Hausdorff distance between Riemannian manifolds. This distance organizes Riemannian manifolds of all possible topological types into a single connected moduli space, where convergence allows the collapse of dimension with unexpectedly rich geometry, as revealed in the work of Cheeger, Fukaya, Gromov and Perelman. Also, Gromov found metric structure within homotopy theory and thus introduced new invariants controlling combinatorial complexity of maps and spaces, such as the simplicial volume, which is responsible for degrees of maps between manifolds. During the same period, Banach spaces and probability theory underwent a geometric metamorphosis, stimulated by the Levy–Milman concentration phenomenon, encompassing the law of large numbers for metric spaces with measures and dimensions going to infinity. The first stages of the new developments were presented in Gromov's course in Paris, which turned into the famous "Green Book" by Lafontaine and Pansu (1979). The present English translation of that work 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
 Language

 eng
 eng
 Edition
 1st ed. 2007.
 Extent
 1 online resource (602 p.)
 Note
 "Reprint of the 2001 edition."
 Contents

 Preface to the French Edition
 Preface to the English Edition
 Introduction: Metrics Everywhere
 Length Structures: Path Metric Spaces
 Degree and Dilatation
 Metric Structures on Families of Metric Spaces
 Convergence and Concentration of Metrics and Measures
 Loewner Rediscovered
 Manifolds with Bounded Ricci Curvature
 Isoperimetric Inequalities and Amenability
 Morse Theory and Minimal Models
 Pinching and Collapse
 Appendix A: 'Quasiconvex' Domains in Rn
 Appendix B: Metric Spaces and Mappings Seen at Many Scales
 Appendix C: Paul Levy's Isoperimetric Inequality
 Appendix D: Systolically Free Manifolds
 Bibliography
 Glossary of Notation
 Index
 Isbn
 9781281377142
 Label
 Metric Structures for Riemannian and NonRiemannian Spaces
 Title
 Metric Structures for Riemannian and NonRiemannian Spaces
 Statement of responsibility
 by Mikhail Gromov ; edited by Jacques LaFontaine, Pierre Pansu
 Language

 eng
 eng
 Summary
 Metric theory has undergone a dramatic phase transition in the last decades when its focus moved from the foundations of real analysis to Riemannian geometry and algebraic topology, to the theory of infinite groups and probability theory. The new wave began with seminal papers by Svarc and Milnor on the growth of groups and the spectacular proof of the rigidity of lattices by Mostow. This progress was followed by the creation of the asymptotic metric theory of infinite groups by Gromov. The structural metric approach to the Riemannian category, tracing back to Cheeger's thesis, pivots around the notion of the Gromov–Hausdorff distance between Riemannian manifolds. This distance organizes Riemannian manifolds of all possible topological types into a single connected moduli space, where convergence allows the collapse of dimension with unexpectedly rich geometry, as revealed in the work of Cheeger, Fukaya, Gromov and Perelman. Also, Gromov found metric structure within homotopy theory and thus introduced new invariants controlling combinatorial complexity of maps and spaces, such as the simplicial volume, which is responsible for degrees of maps between manifolds. During the same period, Banach spaces and probability theory underwent a geometric metamorphosis, stimulated by the Levy–Milman concentration phenomenon, encompassing the law of large numbers for metric spaces with measures and dimensions going to infinity. The first stages of the new developments were presented in Gromov's course in Paris, which turned into the famous "Green Book" by Lafontaine and Pansu (1979). The present English translation of that work 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
 http://library.link/vocab/creatorName
 Gromov, Mikhail
 Dewey number
 516.362
 http://bibfra.me/vocab/relation/httpidlocgovvocabularyrelatorsaut
 _kppQAijlKI
 http://bibfra.me/vocab/relation/httpidlocgovvocabularyrelatorsedt

 Z_jCIFjv3QA
 9ijPHsazZgI
 Language note
 English
 LC call number
 QA641670
 Literary form
 non fiction
 Nature of contents
 dictionaries
 http://library.link/vocab/relatedWorkOrContributorName

 LaFontaine, Jacques.
 Pansu, Pierre.
 Series statement
 Modern Birkhäuser Classics,
 http://library.link/vocab/subjectName

 Global differential geometry
 Cell aggregation
 Algebraic topology
 Mathematics
 Global analysis (Mathematics)
 Differential Geometry
 Manifolds and Cell Complexes (incl. Diff.Topology)
 Algebraic Topology
 Measure and Integration
 Analysis
 Label
 Metric Structures for Riemannian and NonRiemannian Spaces, by Mikhail Gromov ; edited by Jacques LaFontaine, Pierre Pansu, (electronic resource)
 Note
 "Reprint of the 2001 edition."
 Bibliography note
 Includes bibliographical references (p. [545]574) and index
 Carrier category
 online resource
 Carrier category code
 cr
 Content category
 text
 Content type code
 txt
 Contents
 Preface to the French Edition  Preface to the English Edition  Introduction: Metrics Everywhere  Length Structures: Path Metric Spaces  Degree and Dilatation  Metric Structures on Families of Metric Spaces  Convergence and Concentration of Metrics and Measures  Loewner Rediscovered  Manifolds with Bounded Ricci Curvature  Isoperimetric Inequalities and Amenability  Morse Theory and Minimal Models  Pinching and Collapse  Appendix A: 'Quasiconvex' Domains in Rn  Appendix B: Metric Spaces and Mappings Seen at Many Scales  Appendix C: Paul Levy's Isoperimetric Inequality  Appendix D: Systolically Free Manifolds  Bibliography  Glossary of Notation  Index
 Dimensions
 unknown
 Edition
 1st ed. 2007.
 Extent
 1 online resource (602 p.)
 Form of item
 online
 Isbn
 9781281377142
 Media category
 computer
 Media type code
 c
 Other control number
 10.1007/9780817645830
 Specific material designation
 remote
 System control number

 (CKB)1000000000412336
 (EBL)372265
 (OCoLC)184984815
 (SSID)ssj0000202026
 (PQKBManifestationID)11183750
 (PQKBTitleCode)TC0000202026
 (PQKBWorkID)10246030
 (PQKB)10888995
 (DEHe213)9780817645830
 (MiAaPQ)EBC372265
 (EXLCZ)991000000000412336
 Label
 Metric Structures for Riemannian and NonRiemannian Spaces, by Mikhail Gromov ; edited by Jacques LaFontaine, Pierre Pansu, (electronic resource)
 Note
 "Reprint of the 2001 edition."
 Bibliography note
 Includes bibliographical references (p. [545]574) and index
 Carrier category
 online resource
 Carrier category code
 cr
 Content category
 text
 Content type code
 txt
 Contents
 Preface to the French Edition  Preface to the English Edition  Introduction: Metrics Everywhere  Length Structures: Path Metric Spaces  Degree and Dilatation  Metric Structures on Families of Metric Spaces  Convergence and Concentration of Metrics and Measures  Loewner Rediscovered  Manifolds with Bounded Ricci Curvature  Isoperimetric Inequalities and Amenability  Morse Theory and Minimal Models  Pinching and Collapse  Appendix A: 'Quasiconvex' Domains in Rn  Appendix B: Metric Spaces and Mappings Seen at Many Scales  Appendix C: Paul Levy's Isoperimetric Inequality  Appendix D: Systolically Free Manifolds  Bibliography  Glossary of Notation  Index
 Dimensions
 unknown
 Edition
 1st ed. 2007.
 Extent
 1 online resource (602 p.)
 Form of item
 online
 Isbn
 9781281377142
 Media category
 computer
 Media type code
 c
 Other control number
 10.1007/9780817645830
 Specific material designation
 remote
 System control number

 (CKB)1000000000412336
 (EBL)372265
 (OCoLC)184984815
 (SSID)ssj0000202026
 (PQKBManifestationID)11183750
 (PQKBTitleCode)TC0000202026
 (PQKBWorkID)10246030
 (PQKB)10888995
 (DEHe213)9780817645830
 (MiAaPQ)EBC372265
 (EXLCZ)991000000000412336
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<div class="citation" vocab="http://schema.org/"><i class="fa faexternallinksquare fafw"></i> Data from <span resource="http://link.lib.umanitoba.ca/portal/MetricStructuresforRiemannianand/_xlhssVpUaw/" typeof="Book http://bibfra.me/vocab/lite/Item"><span property="name http://bibfra.me/vocab/lite/label"><a href="http://link.lib.umanitoba.ca/portal/MetricStructuresforRiemannianand/_xlhssVpUaw/">Metric Structures for Riemannian and NonRiemannian Spaces, by Mikhail Gromov ; edited by Jacques LaFontaine, Pierre Pansu, (electronic resource)</a></span>  <span property="potentialAction" typeOf="OrganizeAction"><span property="agent" typeof="LibrarySystem http://library.link/vocab/LibrarySystem" resource="http://link.lib.umanitoba.ca/"><span property="name http://bibfra.me/vocab/lite/label"><a property="url" href="http://link.lib.umanitoba.ca/">University of Manitoba Libraries</a></span></span></span></span></div>