Please use this identifier to cite or link to this item:
https://hdl.handle.net/2440/123910
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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 1661-6960 |
Statement of Responsibility: | 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 |
Grant ID: | http://purl.org/au-research/grants/arc/DP170101054 http://purl.org/au-research/grants/arc/FL170100020 http://purl.org/au-research/grants/arc/DE160100525 |
Published version: | https://www.ems-ph.org/journals/journal.php?jrn=jncg |
Appears in Collections: | Aurora harvest 8 Mathematical Sciences publications |
Files in This Item:
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hdl_123910.pdf | Accepted version | 697.57 kB | Adobe PDF | View/Open |
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