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Low-dimensional surgery and the Yamabe invariant

Abstract : 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.
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https://hal.archives-ouvertes.fr/hal-01282155
Contributor : Emmanuel Humbert Connect in order to contact the contributor
Submitted on : Thursday, March 3, 2016 - 1:33:29 PM
Last modification on : Wednesday, February 16, 2022 - 4:55:39 PM

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Bernd Ammann, Mattias Dahl, Emmanuel Humbert. Low-dimensional surgery and the Yamabe invariant. Journal of the Mathematical Society of Japan, Maruzen Company Ltd, 2015, 67 (1), pp.159-182. ⟨10.2969/jmsj/06710159⟩. ⟨hal-01282155⟩

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