Abstract

Given a Galois covering of complete spin manifolds where the base metric has positive scalar curvature near infinity, we prove that for small enough $𝜖>0$, the $𝜖$ spectral projection of the Dirac operator has finite trace in the Atiyah von Neumann algebra. This allows us to define the $L^2$ index in the even case, and we prove its compatibility with the Xie–Yu higher index and deduce $L^2$ versions of the classical Gromov–Lawson relative index theorems. Finally, we briefly discuss some Gromov–Lawson $L^2$ invariants.

Keywords

Mathematical Subject Classification 2010

Milestones

Authors