# Boundary conditions for scalar curvature

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Bernhard Hanke, Universität Augsburg

Online Talk

We show a general deformation principle for boundary conditions of metrics with lower scalar curvature bounds. This implies that  the relaxation of boundary conditions often induces weak homotopy equivalences of spaces of such metrics. Combining this with the existence of fibre bundles over spheres whose total spaces have non-zero $\hat{A}$-genera  we construct compact manifolds for which the spaces of positive scalar curvature metrics with mean convex boundaries have nontrivial higher homotopy groups.