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Type: Journal article
Title: Positive scalar curvature and Poincaré duality for proper actions
Author: Guo, H.
Varghese, M.
Wang, H.
Citation: Journal of Noncommutative Geometry, 2019; 13(4):1381-1433
Publisher: European Mathematical Society
Issue Date: 2019
ISSN: 1661-6952
Statement of
Hao Guo, Varghese Mathai and Hang Wang
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 Poincaré duality between G-equivariant K-homology and K-theory, observing that Poincaré duality does not necessarily hold for general G.
Keywords: Positive scalar curvature; equivariant index theory; equivariant Poincaré duality; proper actions; almost-connected Lie groups; discrete groups; equivariant geometric K-homology; equivariant Spinc-rigidity
Rights: © European Mathematical Society
DOI: 10.4171/JNCG/321
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