LEADER 03898nam 2200625 450 001 9910827647903321 005 20170822144228.0 010 $a1-4704-0597-0 035 $a(CKB)3360000000465167 035 $a(EBL)3114237 035 $a(SSID)ssj0000973338 035 $a(PQKBManifestationID)11552365 035 $a(PQKBTitleCode)TC0000973338 035 $a(PQKBWorkID)10960287 035 $a(PQKB)10269888 035 $a(MiAaPQ)EBC3114237 035 $a(RPAM)16457014 035 $a(PPN)195418727 035 $a(EXLCZ)993360000000465167 100 $a20150416h20102010 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aMetrics of positive scalar curvature and generalised Morse functions$iPart I /$fMark Walsh 210 1$aProvidence, Rhode Island :$cAmerican Mathematical Society,$d2010. 210 4$dİ2010 215 $a1 online resource (80 p.) 225 1 $aMemoirs of the American Mathematical Society,$x0065-9266 ;$vNumber 983 300 $a"Volume 209, number 983 (second of 5 numbers)." 311 $a0-8218-5304-X 320 $aIncludes bibliographical references. 327 $a""Contents""; ""Abstract""; ""Introduction""; ""0.1. Background""; ""0.2. Main results""; ""0.3. The connection with generalised Morse functions and Part II""; ""0.4. Acknowledgements""; ""Chapter 1. Definitions and Preliminary Results""; ""1.1. Isotopy and concordance in the space of metrics of positive scalar curvature""; ""1.2. Warped product metrics on the sphere""; ""1.3. Torpedo metrics on the disk""; ""1.4. Doubly warped products and mixed torpedo metrics""; ""1.5. Inducing a mixed torpedo metric with an embedding""; ""Chapter 2. Revisiting the Surgery Theorem"" 327 $a""2.1. Surgery and cobordism""""2.2. Surgery and positive scalar curvature""; ""2.3. Outline of the proof of Theorem 2.3""; ""2.4. Part 1 of the proof: Curvature formulae for the first deformation""; ""2.5. Part 2 of the proof: A continuous bending argument""; ""2.6. Part 3 of the proof: Isotoping to a standard product""; ""2.7. Applying Theorem 2.3 over a compact family of psc-metrics""; ""2.8. The proof of Theorem 2.2 (The Improved Surgery Theorem)""; ""Chapter 3. Constructing Gromov-Lawson Cobordisms""; ""3.1. Morse Theory and admissible Morse functions"" 327 $a""3.2. A reverse Gromov-Lawson cobordism""""3.3. Continuous families of Morse functions""; ""Chapter 4. Constructing Gromov-Lawson Concordances""; ""4.1. Applying the Gromov-Lawson technique over a pair of cancelling surgeries""; ""4.2. Cancelling Morse critical points: The Weak and Strong Cancellation Theorems""; ""4.3. A strengthening of Theorem 4.2""; ""4.4. Standardising the embedding of the second surgery sphere""; ""Chapter 5. Gromov-Lawson Concordance Implies Isotopy for Cancelling Surgeries""; ""5.1. Connected sums of psc-metrics"" 327 $a""5.2. An analysis of the metric g'', obtained from the second surgery""""5.3. The proof of Theorem 5.1""; ""Chapter 6. Gromov-Lawson Concordance Implies Isotopy in the General Case""; ""6.1. A weaker version of Theorem 0.8""; ""6.2. The proof of the main theorem""; ""Appendix: Curvature Calculations from the Surgery Theorem""; ""Bibliography"" 410 0$aMemoirs of the American Mathematical Society ;$vNumber 983. 606 $aCurvature 606 $aMorse theory 606 $aRiemannian manifolds 606 $aAlgebraic topology 615 0$aCurvature. 615 0$aMorse theory. 615 0$aRiemannian manifolds. 615 0$aAlgebraic topology. 676 $a516.3/62 700 $aWalsh$b Mark $01638685 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910827647903321 996 $aMetrics of positive scalar curvature and generalised Morse functions$93981270 997 $aUNINA