Surgery and the Yamabe invariant

1998/08/11 by Jimmy Petean, Petean, Jimmy, Gabjin Yun +1 · 1 citation
Mathematics · #53C99 #Differential Geometry (math.DG) #FOS: Mathematics #math.DG #msc:53C99

paper · pdf · doi:10.48550/arxiv.math/9808052

14 pages, Latex

arxiv created 1998/08/11 · arxiv updated 2009/11/30

Abstract

We study the Yamabe invariant of manifolds obtained as connected sums along submanifolds of codimension greater than 2. In particular, given a compact smooth manifold M which does not admit metrics of positive scalar curvature, we prove that the Yamabe invariant of M is an upper bound for the Yamabe invariant of any manifold obtained by performing surgery in M on spheres of codimension greater than 2 .

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