Positive Scalar Curvature and Poincare Duality for Proper Actions

Abstract

For G an almost-connected Lie group, we study G-equivariant index theory for proper co-compact actions with various applications, including obstructions to and existence of G-invariant Riemannian metrics of positive scalar curvature. We prove a rigidity result for almost-complex manifolds, generalising Hattori's results, and an analogue of Petrie's conjecture. When G is an almost-connected Lie group or a discrete group, we establish Poincare duality between G-equivariant K-homology and K-theory, observing that Poincare duality does not necessarily hold for general G.

47 pp, final version to appear in JNCG

References in corpus (1)

• On the Strong Novikov Conjecture of Locally Compact Groups for Low Degree Cohomology Classes

Cited by in corpus (7)

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• Orbital integrals and $K$-theory classes
• Equivariant Callias index theory via coarse geometry
• Witten Genus and Elliptic genera for proper actions
• Positive scalar curvature and an equivariant Callias-type index theorem for proper actions
• Higher orbital integrals, rho numbers and index theory
• Higher genera for proper actions of Lie groups, Part 2: the case of manifolds with boundary