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Low-dimensional surgery and the Yamabe invariant
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).ORCID iD: 0000-0002-9184-1467
2015 (English)In: Journal of the Mathematical Society of Japan, ISSN 0025-5645, Vol. 67, no 1, 159-182 p.Article in journal (Refereed) Published
Abstract [en]

Assume that M is a compact n-dimensional manifold and that N is obtained by surgery along a k-dimensional sphere, k <= n - 3. The smooth Yamabe invariants sigma(M) and sigma(N) satisfy sigma(N) >= min(sigma(M), Lambda) for a constant Lambda > 0 depending only on n and k. We derive explicit positive lower bounds for A in dimensions where previous methods failed, namely for (n, k) is an element of {(4, 1), (5, 1), (5, 2), (6, 3), (9, 1), (10, 1)}. With methods from surgery theory and bordism theory several gap phenomena for smooth Yamabe invariants can be deduced.

Place, publisher, year, edition, pages
2015. Vol. 67, no 1, 159-182 p.
Keyword [en]
Yamabe invariant, surgery, symmetrization
National Category
URN: urn:nbn:se:kth:diva-161148DOI: 10.2969/jmsj/06710159ISI: 000348690300005ScopusID: 2-s2.0-84921881989OAI: diva2:796605

QC 20150319

Available from: 2015-03-19 Created: 2015-03-09 Last updated: 2015-03-19Bibliographically approved

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Dahl, Mattias
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