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Surgery and the Spinorial tau-Invariant
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).ORCID iD: 0000-0002-9184-1467
2009 (English)In: Communications in Partial Differential Equations, ISSN 0360-5302, E-ISSN 1532-4133, Vol. 34, no 10, 1147-1179 p.Article in journal (Refereed) Published
Abstract [en]

We associate to a compact spin manifold M a real-valued invariant (M) by taking the supremum over all conformal classes of the infimum inside each conformal class of the first positive Dirac eigenvalue, when the metrics are normalized to unit volume. This invariant is a spinorial analogue of Schoen's sigma-constant, also known as the smooth Yamabe invariant. We prove that if N is obtained from M by surgery of codimension at least 2 then (N) epsilon min{(M), n}, where n is a positive constant depending only on n=dim M. Various topological conclusions can be drawn, in particular that is a spin-bordism invariant below n. Also, below n the values of cannot accumulate from above when varied over all manifolds of dimension n.

Place, publisher, year, edition, pages
2009. Vol. 34, no 10, 1147-1179 p.
Keyword [en]
Dirac operator, Eigenvalue, Surgery, dirac operator, harmonic spinors, eigenvalue
National Category
Mathematics
Identifiers
URN: urn:nbn:se:kth:diva-19200DOI: 10.1080/03605300902769204ISI: 000274420700002Scopus ID: 2-s2.0-70449509362OAI: oai:DiVA.org:kth-19200DiVA: diva2:337247
Note
QC 20100525 QC 20111114Available from: 2010-08-05 Created: 2010-08-05 Last updated: 2017-12-12Bibliographically approved

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Dahl, Mattias

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