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

Abstract

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.

arXiv comment22 pages, 5 EPS figures; fixed problems with bibliography

Cited by in corpus (6)

• Infinite loop spaces and positive scalar curvature
• The Gromov-Lawson-Chernysh surgery theorem
• The positive scalar curvature cobordism category
• On the topology of moduli spaces of non-negatively curved Riemannian metrics
• Cobordism Categories and Parametrized Morse Theory
• Homotopy equivalence of spaces of metrics with invertible Dirac operator