LEADER 04299nam 22007335 450 001 9910300253103321 005 20200701163232.0 010 $a3-0348-0948-4 024 7 $a10.1007/978-3-0348-0948-1 035 $a(CKB)4340000000001626 035 $a(SSID)ssj0001666014 035 $a(PQKBManifestationID)16455069 035 $a(PQKBTitleCode)TC0001666014 035 $a(PQKBWorkID)15000906 035 $a(PQKB)10487452 035 $a(DE-He213)978-3-0348-0948-1 035 $a(MiAaPQ)EBC5575353 035 $a(MiAaPQ)EBC6314758 035 $a(Au-PeEL)EBL5575353 035 $a(OCoLC)1066178944 035 $a(Au-PeEL)EBL6314758 035 $a(OCoLC)1193117501 035 $a(PPN)191478105 035 $a(EXLCZ)994340000000001626 100 $a20151014d2015 u| 0 101 0 $aeng 135 $aurnn|008mamaa 181 $ctxt 182 $cc 183 $acr 200 10$aModuli Spaces of Riemannian Metrics /$fby Wilderich Tuschmann, David J. Wraith 205 $a1st ed. 2015. 210 1$aBasel :$cSpringer Basel :$cImprint: Birkhäuser,$d2015. 215 $a1 online resource (X, 123 p. 3 illus.) 225 1 $aOberwolfach Seminars,$x1661-237X ;$v46 300 $aBibliographic Level Mode of Issuance: Monograph 311 $a3-0348-0947-6 327 $aPart I: Positive scalar curvature -- The (moduli) space of all Riemannian metrics -- Clifford algebras and spin -- Dirac operators and index theorems -- Early results on the space of positive scalar curvature metrics -- Kreck-Stolz invariants -- Applications of Kreck-Stolz invariants -- The eta invariant and applications -- The case of dimensions 2 and 3 -- The observer moduli space and applications -- Other topological structures -- Negative scalar and Ricci curvature -- Part II: Sectional curvature -- Moduli spaces of compact manifolds with positive or non-negative sectional curvature -- Moduli spaces of compact manifolds with negative and non-positive sectional curvature -- Moduli spaces of non-compact manifolds with non-negative sectional curvature -- Positive pinching and the Klingenberg-Sakai conjecture. 330 $aThis book studies certain spaces of Riemannian metrics on both compact and non-compact manifolds. These spaces are defined by various sign-based curvature conditions, with special attention paid to positive scalar curvature and non-negative sectional curvature, though we also consider positive Ricci and non-positive sectional curvature. If we form the quotient of such a space of metrics under the action of the diffeomorphism group (or possibly a subgroup) we obtain a moduli space. Understanding the topology of both the original space of metrics and the corresponding moduli space form the central theme of this book. For example, what can be said about the connectedness or the various homotopy groups of such spaces? We explore the major results in the area, but provide sufficient background so that a non-expert with a grounding in Riemannian geometry can access this growing area of research. 410 0$aOberwolfach Seminars,$x1661-237X ;$v46 606 $aGeometry, Differential 606 $aAlgebraic topology 606 $aManifolds (Mathematics) 606 $aComplex manifolds 606 $aDifferential Geometry$3https://scigraph.springernature.com/ontologies/product-market-codes/M21022 606 $aAlgebraic Topology$3https://scigraph.springernature.com/ontologies/product-market-codes/M28019 606 $aManifolds and Cell Complexes (incl. Diff.Topology)$3https://scigraph.springernature.com/ontologies/product-market-codes/M28027 615 0$aGeometry, Differential. 615 0$aAlgebraic topology. 615 0$aManifolds (Mathematics) 615 0$aComplex manifolds. 615 14$aDifferential Geometry. 615 24$aAlgebraic Topology. 615 24$aManifolds and Cell Complexes (incl. Diff.Topology). 676 $a516.36 700 $aTuschmann$b Wilderich$4aut$4http://id.loc.gov/vocabulary/relators/aut$0755523 702 $aWraith$b David J$4aut$4http://id.loc.gov/vocabulary/relators/aut 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910300253103321 996 $aModuli Spaces of Riemannian Metrics$91898192 997 $aUNINA