Spin-structures and proper group actions

Abstract

We generalise Atiyah and Hirzebruch's vanishing theorem for actions by compact groups on compact Spin-manifolds to possibly noncompact groups acting properly and cocompactly on possibly noncompact Spin-manifolds. As corollaries, we obtain some vanishing results for $\hat{A}$-type genera.

10 pages, revised

References in corpus (1)

• Geometric quantization and families of inner products

Cited by in corpus (6)

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• Positive Scalar Curvature and Poincare Duality for Proper Actions
• Orbital integrals and $K$-theory classes
• Positive scalar curvature and an equivariant Callias-type index theorem for proper actions
• Witten Genus and Elliptic genera for proper actions
• Higher genera for proper actions of Lie groups, Part 2: the case of manifolds with boundary