Computations of the Yamabe invariant

Details Computations of the Yamabe invariant Computations of the Yamabe invariant

1998-08-11

arxiv.org/abs/math/9808053v1

Mathematics

Differential Geometry

10 pages, Latex

Scientific paper

For a compact connected manifold M of dimension n greater than 3 and with no
metric of positive scalar curvature, we prove that the Yamabe invariant is
unchanged under surgery on spheres of dimension different from 1, n-2 and n-1.
We use this result to give new computations of the invariant in dimension four
and display new examples of 4-manifolds which do not admit Einstein metrics.

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