Positive scalar curvature and Poincaré duality for proper actions

DOI10.4171/JNCG/321zbMath1443.53031arXiv1609.01404MaRDI QIDQ2180246

Hao Guo, Hang Wang, Varghese Mathai

Publication date: 13 May 2020

Published in: Journal of Noncommutative Geometry (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1609.01404

zbMATH Keywords

positive scalar curvatureequivariant index theorydiscrete groupsproper actionsequivariant Poincaré dualityalmost-connected Lie groupsequivariant \(\mathrm{Spin}^c\)-rigidityequivariant geometric \(K\)-homology

Mathematics Subject Classification ID

Spin and Spin({}^c) geometry (53C27) Ext and (K)-homology (19K33) Eta-invariants, Chern-Simons invariants (58J28) Kasparov theory ((KK)-theory) (19K35) Equivariant (K)-theory (19L47) Index theory (19K56)

Related Items

Higher genera for proper actions of Lie groups. II: The case of manifolds with boundary ⋮ Equivariant Callias index theory via coarse geometry ⋮ Index of equivariant Callias-type operators and invariant metrics of positive scalar curvature ⋮ An equivariant Poincaré duality for proper cocompact actions by matrix groups ⋮ POSITIVE SCALAR CURVATURE AND CALLIAS-TYPE INDEX THEOREMS FOR PROPER ACTIONS ⋮ Positive scalar curvature and an equivariant Callias-type index theorem for proper actions ⋮ Witten genus and elliptic genera for proper actions ⋮ A vanishing theorem for the Mathai-Zhang index

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Hopf cyclic cohomology and Hodge theory for proper actions
• Elliptic and transversally elliptic index theory from the viewpoint of \(KK\)-theory
• Equivariant geometric K-homology for compact Lie group actions
• Structure and \(K\)-theory of crossed products by proper actions
• \(L^2\)-index formula for proper cocompact group actions
• On the existence of slices for actions of non-compact Lie groups
• Positive scalar curvature and the Dirac operator on complete Riemannian manifolds
• Equivariant Lefschetz maps for simplicial complexes and smooth manifolds
• Quantisation commutes with reduction at discrete series representations of semisimple groups
• Equivariant collaring, tubular neighbourhood and gluing theorems for proper Lie group actions
• On the equivalence of geometric and analytic \(K\)-homology
• The \(L^2\)-index theorem for homogeneous spaces of Lie groups
• The Atiyah-Singer index theorem for families of Dirac operators: Two heat equation proofs
• \(C^ *\)-algebras, positive scalar curvature, and the Novikov conjecture. III
• Equivariant KK-theory and the Novikov conjecture
• An analogue of the Thom isomorphism for crossed products of a C* algebra by an action of R
• Scalar curvature, non-abelian group actions, and the degree of symmetry of exotic spheres
• A geometric construction of the discrete series for semisimple Lie groups
• Extensions of \(C^*\)-algebras and \(K\)-homology
• \(\text{Spin}^c\)-structures and \(S^1\)-actions
• Parallelizability of proper actions, global K-slices and maximal compact subgroups
• Bivariant \(K\)-theory for Banach algebras and the Baum-Connes conjecture
• Groups acting properly on ``bolic spaces and the Novikov conjecture
• The Connes-Kasparov conjecture for almost connected groups and for liner \(p\)-adic groups
• Geometric \(K\)-theory for Lie groups and foliations
• A categorical perspective on the Atiyah-Segal completion theorem in \(KK\)-theory
• Quantising proper actions on \(\text{Spin}^c\)-manifolds
• Cyclic cohomology, the Novikov conjecture and hyperbolic groups
• The scalar curvature on totally geodesic fiberings
• Bivariant K-theory via correspondences
• Geometric quantization and families of inner products
• The fundamental equations of a submersion
• The index of elliptic operators. I
• Totally geodesic maps
• Equivariant \(K\)-theory and completion
• Geometric quantization for proper actions
• A Geometric Description of Equivariant K-Homology for Proper Actions
• A Sufficient Condition that a Mapping of Riemannian Manifolds be a Fibre Bundle
• TOPOLOGICAL INVARIANTS OF ELLIPTIC OPERATORS. I:K-HOMOLOGY
• Callias-type operators in C∗-algebras and positive scalar curvature on noncompact manifolds
• Quantisation of presymplectic manifolds, $K$-theory and group representations
• FREDHOLM COMPLEXES
• Smooth 𝑆¹ actions on homotopy complex projective spaces and related topics
• The completion theorem in \(K\)-theory for proper actions of a discrete group
• Spin-structures and proper group actions