For an almost-connected Lie group, we study -equivariant index theory for proper co-compact actions with various applications, including obstructions to and existence of -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 is an almost-connected Lie group or a discrete group, we establish Poincaré duality between -equivariant -homology and -theory, observing that Poincaré duality does not necessarily hold for general .
Cite this article
Hao Guo, Varghese Mathai, Hang Wang, Positive scalar curvature and Poincaré duality for proper actions. J. Noncommut. Geom. 13 (2019), no. 4, pp. 1381–1433DOI 10.4171/JNCG/321