Details

Autor(en) / Beteiligte

• Guo, Hao
• Xie, Zhizhang
• Yu, Guoliang

Titel

A Lichnerowicz vanishing theorem for the maximal Roe algebra

Ist Teil von

• Mathematische annalen, 2023-02, Vol.385 (1-2), p.717-743

Ort / Verlag

Berlin/Heidelberg: Springer Berlin Heidelberg

Erscheinungsjahr

2023

Quelle

SpringerLink

Beschreibungen/Notizen

• We show that if a countable discrete group acts properly and isometrically on a spin manifold of bounded Riemannian geometry and uniformly positive scalar curvature, then, under a suitable condition on the group action, the maximal higher index of the Dirac operator vanishes in K -theory of the maximal equivariant Roe algebra. The group action is not assumed to be cocompact. A key step in the proof is to establish a functional calculus for the Dirac operator in the maximal equivariant uniform Roe algebra. This allows us to prove vanishing of the index of the Dirac operator in K -theory of this algebra, which in turn yields the result for the maximal higher index.