Abstract
AbstractWe present a rigidity theorem for the action of the mapping class group $$\pi _0({\mathrm{Diff}}(M))$$
π
0
(
Diff
(
M
)
)
on the space $$\mathcal {R}^+(M)$$
R
+
(
M
)
of metrics of positive scalar curvature for high dimensional manifolds M. This result is applicable to a great number of cases, for example to simply connected 6-manifolds and high dimensional spheres. Our proof is fairly direct, using results from parametrised Morse theory, the 2-index theorem and computations on certain metrics on the sphere. We also give a non-triviality criterion and a classification of the action for simply connected 7-dimensional $${\mathrm{Spin}}$$
Spin
-manifolds.
Funder
Deutsche Forschungsgemeinschaft
Publisher
Springer Science and Business Media LLC
Reference34 articles.
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