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Positive scalar curvature and Poincaré duality for proper actions

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dc.contributor.authorGuo, H.
dc.contributor.authorVarghese, M.
dc.contributor.authorWang, H.
dc.date.issued2019
dc.description.abstractFor 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.
dc.description.statementofresponsibilityHao Guo, Varghese Mathai and Hang Wang
dc.identifier.citationJournal of Noncommutative Geometry, 2019; 13(4):1381-1433
dc.identifier.doi10.4171/JNCG/321
dc.identifier.issn1661-6952
dc.identifier.issn1661-6960
dc.identifier.orcidVarghese, M. [0000-0002-1100-3595]
dc.identifier.urihttp://hdl.handle.net/2440/123910
dc.language.isoen
dc.publisherEuropean Mathematical Society
dc.relation.granthttp://purl.org/au-research/grants/arc/DP170101054
dc.relation.granthttp://purl.org/au-research/grants/arc/FL170100020
dc.relation.granthttp://purl.org/au-research/grants/arc/DE160100525
dc.rights© European Mathematical Society
dc.source.urihttps://www.ems-ph.org/journals/journal.php?jrn=jncg
dc.subjectPositive scalar curvature; equivariant index theory; equivariant Poincaré duality; proper actions; almost-connected Lie groups; discrete groups; equivariant geometric K-homology; equivariant Spinc-rigidity
dc.titlePositive scalar curvature and Poincaré duality for proper actions
dc.typeJournal article
pubs.publication-statusPublished

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