Circle actions and Z/k-manifolds

2003/06/30 by Weiping Zhang
Mathematics · #math.DG #math.AT #msc:57R #msc:58G

paper · pdf

published as C. R. Acad. Sci. Paris, Ser. I, 337 (2003), 57-60 · 6 pages. Minor changes for the published version

arxiv created 2003/07/05 · arxiv updated 2009/11/30

Abstract

We establish an S¹-equivariant index theorem for Dirac operators on Z/k-manifolds. As an application, we generalize the Atiyah-Hirzebruch vanishing theorem for S¹-actions on closed spin manifolds to the case of Z/k-manifolds.

Related

• Rigidity and Vanishing Theorems on ℤ/k Spin^c manifolds
• An equivariant index for proper actions III: the invariant and discrete series indices
• Index theorem for equivariant Dirac operators on non-compact manifolds
• A short proof of an index theorem, II
• An equivariant index for proper actions II: properties and applications