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Some applications of dirac operators and eta invariants in geometry
KTH, Superseded Departments, Mathematics.ORCID iD: 0000-0002-9184-1467
1999 (English)Doctoral thesis, comprehensive summary (Other scientific)
Place, publisher, year, edition, pages
Stockholm: KTH , 1999. , 16 p.
National Category
Mathematics
Identifiers
URN: urn:nbn:se:kth:diva-2788ISBN: 99-2952627-7 OAI: oai:DiVA.org:kth-2788DiVA: diva2:8501
Public defence
1999-05-01, 00:00 (English)
Note
QC 20100525Available from: 2000-01-01 Created: 2000-01-01 Last updated: 2010-05-26Bibliographically approved
List of papers
1. scalar curvature rigidity for asymptotically locally hyperbolic manifolds
Open this publication in new window or tab >>scalar curvature rigidity for asymptotically locally hyperbolic manifolds
1998 (English)In: Annals of Global Analysis and Geometry, ISSN 0232-704X, E-ISSN 1572-9060, Vol. 16, 1-27 p.Article in journal (Refereed) Published
Abstract [en]

Rigidity results for asymptotically locally hyperbolic manifoldswith lower bounds on scalar curvature are proved using spinor methodsrelated to the Witten proof of the positive mass theorem. The argument isbased on a study of the Dirac operator defined with respect to the Killingconnection. The existence of asymptotic Killing spinors is related to thespin structure on the end. The expression for the mass is calculated andproven to vanish for conformally compact Einstein manifolds with conformalboundary a spherical space form, giving rigidity. In the 4-dimensional case,the signature of the manifold is related to the spin structure on the end andexplicit formulas for the relevant invariants are given.

National Category
Mathematics
Identifiers
urn:nbn:se:kth:diva-13070 (URN)
Note
QC 20100525Available from: 2010-05-26 Created: 2010-05-26 Last updated: 2017-12-12Bibliographically approved
2. The Positive Mass Theorem for Ale Manifolds
Open this publication in new window or tab >>The Positive Mass Theorem for Ale Manifolds
1997 (English)In: Mathematics of gravitation. P. 1: Lorentzian geometry and Einstein equations / [ed] Piotr T. Chruściel, 1997Conference paper, Published paper (Other academic)
Series
* Banach center publications, ISSN 0137-6934 ; 41:1411
National Category
Mathematics
Identifiers
urn:nbn:se:kth:diva-13071 (URN)
Conference
Mathematical Aspects of Theories of Gravitation
Note
QC 20100526Available from: 2010-05-26 Created: 2010-05-26 Last updated: 2010-05-26Bibliographically approved
3. Dependence on the spin structure of the eta and Rokhlin invariants
Open this publication in new window or tab >>Dependence on the spin structure of the eta and Rokhlin invariants
2002 (English)In: Topology and its Applications, ISSN 0166-8641, E-ISSN 1879-3207, Vol. 118, no 3, 345-355 p.Article in journal (Refereed) Published
Abstract [en]

We study the dependence of the eta invariant etaD on the spin structure, where D is a twisted Dirac operator on a (4k + 3)-dimensional spin manifold. The difference between the eta invariants for two spin structures related by a cohomology class which is the reduction of a H-1 (M, Z)-class is shown to be a half integer. As an application of the technique of proof the generalized Rokhlin invariant is shown to be equal modulo 8 for two spin structures related in this way.

Keyword
spin structure, Dirac operator, eta invariant, Rokhlin invariant
National Category
Mathematics
Identifiers
urn:nbn:se:kth:diva-13072 (URN)000173378300006 ()
Note
QC 20100526Available from: 2010-05-26 Created: 2010-05-26 Last updated: 2017-12-12Bibliographically approved

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Dahl, Mattias

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