JournalsjncgVol. 13, No. 4pp. 1381–1433

Positive scalar curvature and Poincaré duality for proper actions

  • Hao Guo

    Texas A&M University, College Station, USA
  • Varghese Mathai

    University of Adelaide, Australia
  • Hang Wang

    East China Normal University, Shanghai, China
Positive scalar curvature and Poincaré duality for proper actions cover
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Abstract

For GG an almost-connected Lie group, we study GG-equivariant index theory for proper co-compact actions with various applications, including obstructions to and existence of GG-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 GG is an almost-connected Lie group or a discrete group, we establish Poincaré duality between GG-equivariant KK-homology and KK-theory, observing that Poincaré duality does not necessarily hold for general GG.

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. 1381–1433

DOI 10.4171/JNCG/321