Guo, H.Varghese, M.Wang, H.2020-03-302020-03-302019Journal of Noncommutative Geometry, 2019; 13(4):1381-14331661-69521661-6960http://hdl.handle.net/2440/123910For 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 Poincaré duality between G-equivariant K-homology and K-theory, observing that Poincaré duality does not necessarily hold for general G.en© European Mathematical SocietyPositive scalar curvature; equivariant index theory; equivariant Poincaré duality; proper actions; almost-connected Lie groups; discrete groups; equivariant geometric K-homology; equivariant Spinc-rigidityJournal article003008455710.4171/JNCG/3210005481672000052-s2.0-85079180441367296Varghese, M. [0000-0002-1100-3595]