Matches in SemOpenAlex for { <https://semopenalex.org/work/W3048804837> ?p ?o ?g. }
Showing items 1 to 61 of
61
with 100 items per page.
- W3048804837 abstract "The aim of this dissertation is to use relative higher index theory to studyquestions of existence and classification of positive scalar curvature metricson manifolds with boundary. First we prove a theorem relating the higherindex of a manifold with boundary endowed with a Riemannian metric whichis collared at the boundary and has positive scalar curvature there, to therelative higher index as defined by Chang, Weinberger and Yu. Next, wedefine relative higher rho-invariants associated to positive scalar curvaturemetrics on manifolds with boundary, which are collared at boundary. Inorder to do this, we define variants of Roe and localisation algebras for spaceswith cylindrical ends and use this to obtain an analogue of the Higson-Roeanalytic surgery sequence for manifolds with boundary. This is followedby a comparison of our definition of the relative index with that of Chang,Weinberger and Yu. The higher rho-invariants can be used to classify positivescalar curvature metrics up to concordance and bordism. In order to showthe effectiveness of the machinery developed here, we use it to give a simpleproof of the aforementioned statement regarding the relationship of indicesdefined in the presence of positive scalar curvature at the boundary and therelative higher index. We also devote a few sections to address technicalissues regarding maximal Roe and structure algebras and a maximal versionof Paschke duality, whose solutions was lacking in the literature." @default.
- W3048804837 created "2020-08-18" @default.
- W3048804837 creator A5080416253 @default.
- W3048804837 date "2020-07-24" @default.
- W3048804837 modified "2023-09-27" @default.
- W3048804837 title "Index Theory and Positive Scalar Curvature" @default.
- W3048804837 hasPublicationYear "2020" @default.
- W3048804837 type Work @default.
- W3048804837 sameAs 3048804837 @default.
- W3048804837 citedByCount "0" @default.
- W3048804837 crossrefType "dissertation" @default.
- W3048804837 hasAuthorship W3048804837A5080416253 @default.
- W3048804837 hasConcept C12520029 @default.
- W3048804837 hasConcept C134306372 @default.
- W3048804837 hasConcept C14196021 @default.
- W3048804837 hasConcept C195065555 @default.
- W3048804837 hasConcept C197617374 @default.
- W3048804837 hasConcept C202444582 @default.
- W3048804837 hasConcept C2524010 @default.
- W3048804837 hasConcept C33923547 @default.
- W3048804837 hasConcept C42448751 @default.
- W3048804837 hasConcept C57691317 @default.
- W3048804837 hasConcept C62354387 @default.
- W3048804837 hasConceptScore W3048804837C12520029 @default.
- W3048804837 hasConceptScore W3048804837C134306372 @default.
- W3048804837 hasConceptScore W3048804837C14196021 @default.
- W3048804837 hasConceptScore W3048804837C195065555 @default.
- W3048804837 hasConceptScore W3048804837C197617374 @default.
- W3048804837 hasConceptScore W3048804837C202444582 @default.
- W3048804837 hasConceptScore W3048804837C2524010 @default.
- W3048804837 hasConceptScore W3048804837C33923547 @default.
- W3048804837 hasConceptScore W3048804837C42448751 @default.
- W3048804837 hasConceptScore W3048804837C57691317 @default.
- W3048804837 hasConceptScore W3048804837C62354387 @default.
- W3048804837 hasLocation W30488048371 @default.
- W3048804837 hasOpenAccess W3048804837 @default.
- W3048804837 hasPrimaryLocation W30488048371 @default.
- W3048804837 hasRelatedWork W1543390268 @default.
- W3048804837 hasRelatedWork W2043179113 @default.
- W3048804837 hasRelatedWork W2170137214 @default.
- W3048804837 hasRelatedWork W2518825557 @default.
- W3048804837 hasRelatedWork W2887637854 @default.
- W3048804837 hasRelatedWork W2925324957 @default.
- W3048804837 hasRelatedWork W2949754773 @default.
- W3048804837 hasRelatedWork W2951732614 @default.
- W3048804837 hasRelatedWork W2952908485 @default.
- W3048804837 hasRelatedWork W2996308506 @default.
- W3048804837 hasRelatedWork W3010851246 @default.
- W3048804837 hasRelatedWork W3045942313 @default.
- W3048804837 hasRelatedWork W3082017470 @default.
- W3048804837 hasRelatedWork W3099226805 @default.
- W3048804837 hasRelatedWork W3099234690 @default.
- W3048804837 hasRelatedWork W3103199746 @default.
- W3048804837 hasRelatedWork W3104352874 @default.
- W3048804837 hasRelatedWork W3104427530 @default.
- W3048804837 hasRelatedWork W3105143363 @default.
- W3048804837 hasRelatedWork W3177072527 @default.
- W3048804837 isParatext "false" @default.
- W3048804837 isRetracted "false" @default.
- W3048804837 magId "3048804837" @default.
- W3048804837 workType "dissertation" @default.