Index theory and deformations of open nonnegatively curved manifolds

2018/05/06 by Belegradek, Igor
#53C21 #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1805.02239

Abstract

We use an index-theoretic technique of Hitchin to show that the space of complete Riemannian metrics of nonnegative sectional curvature on certain open spin manifolds has nontrivial homotopy groups in infinitely many degrees. A new ingredient of independent interest is homotopy density of the subspace of metrics with cylindrical ends.

Related

• Index theory with bounded geometry, the uniformly finite A-hat class, and infinite connected sums
• Moduli spaces of nonnegatively curved metrics on exotic spheres
• Space of nonnegatively curved metrics and pseudoisotopies
• Positive scalar curvature, K-area and essentialness
• Index theory and partitioning by enlargeable hypersurfaces