Positive scalar curvature and Poincaré duality for proper actions
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(Accepted version)
Date
2019
Authors
Guo, H.
Varghese, M.
Wang, H.
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Journal of Noncommutative Geometry, 2019; 13(4):1381-1433
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Hao Guo, Varghese Mathai and Hang Wang
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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.
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© European Mathematical Society