Matches in SemOpenAlex for { <https://semopenalex.org/work/W1575620451> ?p ?o ?g. }
Showing items 1 to 83 of
83
with 100 items per page.
- W1575620451 abstract "In this thesis we study the zeta function formalism of finitely summable spectral triples in noncommutative geometry introduced by Alain Connes in 1995. In particular we study how these zeta functions, that naturally come in different classes, can be used to classify objects. The thesis starts with the study of finite, connected, unoriented graphs with Betti number at least 2 and valencies at least 3. We start by constructing a finitely summable spectral triple for these and prove that the first class of zeta functions determines the graph. Next closed smooth Riemannian manifolds are studied. The ideas of finitely summable spectral triples are applied to the Laplacian. We prove that the first class together with the diagonal of the second class of zeta functions determines the Riemannian manifold. This is in contrast with the usual zeta function where the phenomenon of isospectrality occurs: different objects can have the same spectrum (which is equivalent of having the same usual zeta function). Finally, the last result is formalized by introducing the concept of length categories and distances. We construct the length of a smooth map between smooth Riemannian manifolds and this in turn induces a distance between them. We conclude by proving that this distance induces the topology of uniform convergence of smooth Riemannian manifolds." @default.
- W1575620451 created "2016-06-24" @default.
- W1575620451 creator A5036714508 @default.
- W1575620451 date "2008-06-01" @default.
- W1575620451 modified "2023-09-26" @default.
- W1575620451 title "Zeta function rigidity. A view from noncommutative geometry" @default.
- W1575620451 cites W1516418562 @default.
- W1575620451 cites W1553525724 @default.
- W1575620451 cites W1980942321 @default.
- W1575620451 cites W1989214109 @default.
- W1575620451 cites W1992081887 @default.
- W1575620451 cites W2014423354 @default.
- W1575620451 cites W2016021508 @default.
- W1575620451 cites W2027842332 @default.
- W1575620451 cites W2320810720 @default.
- W1575620451 cites W2324642910 @default.
- W1575620451 cites W2326825004 @default.
- W1575620451 cites W2962729560 @default.
- W1575620451 hasPublicationYear "2008" @default.
- W1575620451 type Work @default.
- W1575620451 sameAs 1575620451 @default.
- W1575620451 citedByCount "0" @default.
- W1575620451 crossrefType "dissertation" @default.
- W1575620451 hasAuthorship W1575620451A5036714508 @default.
- W1575620451 hasConcept C127413603 @default.
- W1575620451 hasConcept C129621563 @default.
- W1575620451 hasConcept C134306372 @default.
- W1575620451 hasConcept C181104567 @default.
- W1575620451 hasConcept C202444582 @default.
- W1575620451 hasConcept C2524010 @default.
- W1575620451 hasConcept C2779593128 @default.
- W1575620451 hasConcept C29384965 @default.
- W1575620451 hasConcept C33923547 @default.
- W1575620451 hasConcept C35235930 @default.
- W1575620451 hasConcept C35861355 @default.
- W1575620451 hasConcept C49976459 @default.
- W1575620451 hasConcept C51364350 @default.
- W1575620451 hasConcept C529865628 @default.
- W1575620451 hasConcept C68797384 @default.
- W1575620451 hasConcept C78519656 @default.
- W1575620451 hasConceptScore W1575620451C127413603 @default.
- W1575620451 hasConceptScore W1575620451C129621563 @default.
- W1575620451 hasConceptScore W1575620451C134306372 @default.
- W1575620451 hasConceptScore W1575620451C181104567 @default.
- W1575620451 hasConceptScore W1575620451C202444582 @default.
- W1575620451 hasConceptScore W1575620451C2524010 @default.
- W1575620451 hasConceptScore W1575620451C2779593128 @default.
- W1575620451 hasConceptScore W1575620451C29384965 @default.
- W1575620451 hasConceptScore W1575620451C33923547 @default.
- W1575620451 hasConceptScore W1575620451C35235930 @default.
- W1575620451 hasConceptScore W1575620451C35861355 @default.
- W1575620451 hasConceptScore W1575620451C49976459 @default.
- W1575620451 hasConceptScore W1575620451C51364350 @default.
- W1575620451 hasConceptScore W1575620451C529865628 @default.
- W1575620451 hasConceptScore W1575620451C68797384 @default.
- W1575620451 hasConceptScore W1575620451C78519656 @default.
- W1575620451 hasLocation W15756204511 @default.
- W1575620451 hasOpenAccess W1575620451 @default.
- W1575620451 hasPrimaryLocation W15756204511 @default.
- W1575620451 hasRelatedWork W180996893 @default.
- W1575620451 hasRelatedWork W1966549421 @default.
- W1575620451 hasRelatedWork W2029502251 @default.
- W1575620451 hasRelatedWork W2282328185 @default.
- W1575620451 hasRelatedWork W2321077357 @default.
- W1575620451 hasRelatedWork W2420750987 @default.
- W1575620451 hasRelatedWork W2529940907 @default.
- W1575620451 hasRelatedWork W2949767669 @default.
- W1575620451 hasRelatedWork W2950576054 @default.
- W1575620451 hasRelatedWork W2951790277 @default.
- W1575620451 hasRelatedWork W2963023087 @default.
- W1575620451 hasRelatedWork W2963401460 @default.
- W1575620451 hasRelatedWork W3005309422 @default.
- W1575620451 hasRelatedWork W3098540368 @default.
- W1575620451 hasRelatedWork W3098911118 @default.
- W1575620451 hasRelatedWork W3103266804 @default.
- W1575620451 hasRelatedWork W3105348649 @default.
- W1575620451 hasRelatedWork W3133333264 @default.
- W1575620451 hasRelatedWork W3138066140 @default.
- W1575620451 hasRelatedWork W3161085241 @default.
- W1575620451 isParatext "false" @default.
- W1575620451 isRetracted "false" @default.
- W1575620451 magId "1575620451" @default.
- W1575620451 workType "dissertation" @default.