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Generalized Surgery on Riemannian Manifolds of Positive Ricci Curvature

Reiser, Philipp 1
1 Institut für Algebra und Geometrie (IAG), Karlsruher Institut für Technologie (KIT)

Abstract (englisch):

The surgery theorem of Wraith states that the existence of metrics of positive Ricci curvature is preserved under surgery if certain metric and dimensional conditions are satisfied. We generalize this theorem by relaxing the conditions on the dimensions involved and by generalizing the surgery construction itself. As applications we construct metrics of positive Ricci curvature on manifolds obtained by plumbing. Specifically, this construction provides an extension of a result of Burdick on the existence of metrics of positive Ricci curvature on connected sums of linear sphere bundles, and, moreover, it yields infinite families of new examples of manifolds with a metric of positive Ricci curvature in all dimensions divisible by 6.


Volltext §
DOI: 10.5445/IR/1000150280
Veröffentlicht am 05.09.2022
Cover der Publikation
Zugehörige Institution(en) am KIT Institut für Algebra und Geometrie (IAG)
Publikationstyp Hochschulschrift
Publikationsdatum 05.09.2022
Sprache Englisch
Identifikator KITopen-ID: 1000150280
Verlag Karlsruher Institut für Technologie (KIT)
Umfang v, 136 S.
Art der Arbeit Dissertation
Fakultät Fakultät für Mathematik (MATH)
Institut Institut für Algebra und Geometrie (IAG)
Prüfungsdatum 21.07.2022
Referent/Betreuer Tuschmann, Wilderich
Leuzinger, Enrico
Galaz-Garcia, Fernando
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