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You searched for subject:(manifolds with corners). Showing records 1 – 3 of 3 total matches.

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University of Oregon

1. Burdick, Bradley. Metrics of Positive Ricci Curvature on Connected Sums: Projective Spaces, Products, and Plumbings.

Degree: PhD, Department of Mathematics, 2019, University of Oregon

The classification of simply connected manifolds admitting metrics of positive scalar curvature of initiated by Gromov-Lawson, at its core, relies on a careful geometric construction that preserves positive scalar curvature under surgery and, in particular, under connected sum. For simply connected manifolds admitting metrics of positive Ricci curvature, it is conjectured that a similar classification should be possible, and, in particular, there is no suspected obstruction to preserving positive Ricci curvature under connected sum. Yet there is no general construction known to take two Ricci-positive Riemannian manifolds and form a Ricci-positive metric on their connected sums. In this work, we utilize and extend Perelman’s construction of Ricci-positive metrics on connected sums of complex projective planes, to give an explicit construction of Ricci-positive metrics on connected sums given that the individual summands admit very specific Ricci- positive metrics, which we call core metrics. Working towards the new goal of constructing core metrics on manifolds known to support metrics of positive Ricci curvature: we show how to generalize Perelman’s construction to all projective spaces, we show that the existence of core metrics is preserved under iterated sphere bundles, and we construct core metrics on certain boundaries of plumbing disk bundles over spheres. These constructions come together to give many new examples of Ricci-positive connected sums, in particular on the connected sum of arbitrary products of spheres and on exotic projective spaces. Advisors/Committee Members: Botvinnik, Boris (advisor).

Subjects/Keywords: connected sums; manifolds with corners; positive Ricci curvature; Riemannian geometry; splines; surgery

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APA (6th Edition):

Burdick, B. (2019). Metrics of Positive Ricci Curvature on Connected Sums: Projective Spaces, Products, and Plumbings. (Doctoral Dissertation). University of Oregon. Retrieved from https://scholarsbank.uoregon.edu/xmlui/handle/1794/24879

Chicago Manual of Style (16th Edition):

Burdick, Bradley. “Metrics of Positive Ricci Curvature on Connected Sums: Projective Spaces, Products, and Plumbings.” 2019. Doctoral Dissertation, University of Oregon. Accessed January 19, 2021. https://scholarsbank.uoregon.edu/xmlui/handle/1794/24879.

MLA Handbook (7th Edition):

Burdick, Bradley. “Metrics of Positive Ricci Curvature on Connected Sums: Projective Spaces, Products, and Plumbings.” 2019. Web. 19 Jan 2021.

Vancouver:

Burdick B. Metrics of Positive Ricci Curvature on Connected Sums: Projective Spaces, Products, and Plumbings. [Internet] [Doctoral dissertation]. University of Oregon; 2019. [cited 2021 Jan 19]. Available from: https://scholarsbank.uoregon.edu/xmlui/handle/1794/24879.

Council of Science Editors:

Burdick B. Metrics of Positive Ricci Curvature on Connected Sums: Projective Spaces, Products, and Plumbings. [Doctoral Dissertation]. University of Oregon; 2019. Available from: https://scholarsbank.uoregon.edu/xmlui/handle/1794/24879


Université de Lorraine

2. Mougel, Jérémy. Analysis on singular space and operators algebras : Analyse sur les espaces singuliers et algèbres d’opérateurs.

Degree: Docteur es, Mathématiques, 2019, Université de Lorraine

Nous étudions l'opérateur H=-Δ +V qui représente l'énergie d'un système à N-électrons. Pour cela, nous utilisons les algèbres d'opérateurs. Nous commençons par définir une C*-algèbres A qui contient le potentiel V du problème puis nous prenons son produit croisé AxX . Les résolvantes de H sont ainsi contenues dans cette C*algèbre dans AxX. Par une étude précise du spectre de AxX, nous obtenons une décomposition spectrale essentiel de H et donc un résultat qui étend le théorème HV Z dans la continuité des travaux de V. Georgescu. Nous étendons ce résultat en remplaçant l'espace euclidien X par le groupe de Heisenberg. Dans la seconde partie de la thèse, nous montrons que le spectre de la C*-algèbre A et un espace introduit par A. Vasy dans les années 2000 sont les mêmes. L'espace construit par A. Vasy est construit par éclatements successifs d'une variété différentielle à coins. La preuve repose également sur des résultats d'éclatements de variétés. En particulier, nous avons introduit la notion de « graph blow-up »' d'une variété par rapport à une famille assez générale de sous-variétés.

We study the operator H=-Δ +V that describes the energy of a system with N electrons. To do this, we use operator algebras. We thus first define a C*algebra A that contains the potentials V of the problem and then consider the crossed product AxX. The resolvents of H then belong to the C*algebra AxX. By a precise study of the spectrum of AxX, we obtain a decomposition of the essential spectrum of H, and hence of result that extends the HVZ theorem, in the spirit of Georgescu. We extend these results by replacing the underlying Euclidean space X with the Heisenberg group. In the second part of the thesis, we show that the spectrum of A and the space introduce by A. Vasy around the year 2000 are the same. The space introduced by A. Vasy is defined using the blow-up of differentials manifolds with corners. The proofs are based on some differential geometric results on blow-ups of manifolds, in particular, we introduce the notion of ``graph blow-up'' of a manifold with respect to a rather general family of submanifolds.

Advisors/Committee Members: Nistor, Victor (thesis director).

Subjects/Keywords: Espaces singuliers; Algèbres d'opérateurs; Variétés à coins; Singular spaces; Operator algebras; Manifolds with corners,; 512.556

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6th Edition):

Mougel, J. (2019). Analysis on singular space and operators algebras : Analyse sur les espaces singuliers et algèbres d’opérateurs. (Doctoral Dissertation). Université de Lorraine. Retrieved from http://www.theses.fr/2019LORR0263

Chicago Manual of Style (16th Edition):

Mougel, Jérémy. “Analysis on singular space and operators algebras : Analyse sur les espaces singuliers et algèbres d’opérateurs.” 2019. Doctoral Dissertation, Université de Lorraine. Accessed January 19, 2021. http://www.theses.fr/2019LORR0263.

MLA Handbook (7th Edition):

Mougel, Jérémy. “Analysis on singular space and operators algebras : Analyse sur les espaces singuliers et algèbres d’opérateurs.” 2019. Web. 19 Jan 2021.

Vancouver:

Mougel J. Analysis on singular space and operators algebras : Analyse sur les espaces singuliers et algèbres d’opérateurs. [Internet] [Doctoral dissertation]. Université de Lorraine; 2019. [cited 2021 Jan 19]. Available from: http://www.theses.fr/2019LORR0263.

Council of Science Editors:

Mougel J. Analysis on singular space and operators algebras : Analyse sur les espaces singuliers et algèbres d’opérateurs. [Doctoral Dissertation]. Université de Lorraine; 2019. Available from: http://www.theses.fr/2019LORR0263


University of Western Ontario

3. Huang, Jianing. Syzygy Order of Big Polygon Spaces.

Degree: 2018, University of Western Ontario

For a compact smooth manifold with a torus action, its equivariant cohomology is a finitely generated module over a polynomial ring encoding information about the space and the action. For such a module, we can associate a purely algebraic notion called syzygy order. Syzygy order of equivariant cohomology is closely related to the exactness of Atiyah-Bredon sequence in equivariant cohomology. In this thesis we study a family of compact orientable manifolds with torus actions called big polygon spaces. We compute the syzygy orders of their equivariant cohomologies. The main tool used is a quotient criterion for syzygies in equivariant cohomology. We also generalize a lacunary principle for Morse-Bott functions to manifolds with corners in the process of computation. Some applications of the main result are discussed in the end.

Subjects/Keywords: Big polygon spaces; equivariant cohomology; syzygy; quotient criterion; manifolds with corners; Morse theory; Geometry and Topology

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6th Edition):

Huang, J. (2018). Syzygy Order of Big Polygon Spaces. (Thesis). University of Western Ontario. Retrieved from https://ir.lib.uwo.ca/etd/5643

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16th Edition):

Huang, Jianing. “Syzygy Order of Big Polygon Spaces.” 2018. Thesis, University of Western Ontario. Accessed January 19, 2021. https://ir.lib.uwo.ca/etd/5643.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7th Edition):

Huang, Jianing. “Syzygy Order of Big Polygon Spaces.” 2018. Web. 19 Jan 2021.

Vancouver:

Huang J. Syzygy Order of Big Polygon Spaces. [Internet] [Thesis]. University of Western Ontario; 2018. [cited 2021 Jan 19]. Available from: https://ir.lib.uwo.ca/etd/5643.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Huang J. Syzygy Order of Big Polygon Spaces. [Thesis]. University of Western Ontario; 2018. Available from: https://ir.lib.uwo.ca/etd/5643

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

.