On the homotopy type of the space $\mathcal{R}^+(M)$

Details On the homotopy type of the space $\mathcal{R}^+(M)$ On the homotopy type of the space $\mathcal{R}^+(M)$

2004-05-13

arxiv.org/abs/math/0405235v2

Mathematics

Geometric Topology

22 pages, 5 EPS figures; fixed problems with bibliography

Scientific paper

we show that the space of metrics of positive scalar curvature on a manifold is, when nonempty, homotopy equivalent to a space of metrics of positive scalar curvature that restrict to a fixed metric near a given submanifold of codimension greater or equal than 3. Our main tool is a parameterized version of the Gromov-Lawson construction, which was used to show that the existence of a metric of positive scalar curvature on a manifold was invariant under surgeries in codimension greater or equal than 3.

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