Abstract.
We study the Yamabe invariant of manifolds obtained as connected sums along submanifolds of codimension greater than 2. In particular: for a compact connected manifold M with no metric of positive scalar curvature, we prove that the Yamabe invariant of any manifold obtained by performing surgery on spheres of codimension greater than 2 on M is not smaller than the invariant of M.
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Submitted: August 1998.
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Petean, J., Yun, G. Surgery and the Yamabe Invariant . GAFA, Geom. funct. anal. 9, 1189–1199 (1999). https://doi.org/10.1007/s000390050112
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DOI: https://doi.org/10.1007/s000390050112