An analytic \(LT\)-equivariant index and noncommutative geometry

DOI10.4171/JNCG/330zbMath1429.58019arXiv1701.06055OpenAlexW2960560761MaRDI QIDQ2327771

Doman Takata

Publication date: 15 October 2019

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

Full work available at URL: https://arxiv.org/abs/1701.06055

zbMATH Keywords

Dirac operatorsloop groupsspectral triplescrossed product algebrasinfinite-dimensional manifolds

Mathematics Subject Classification ID

Loop groups and related constructions, group-theoretic treatment (22E67) Exotic index theories on manifolds (58J22) Noncommutative geometry (à la Connes) (58B34)

Related Items

Geometric \(K\)-homology and the Freed-Hopkins-Teleman theorem ⋮ \(LT\)-equivariant index from the viewpoint of \(KK\)-theory. A global analysis on the infinite-dimensional Heisenberg group ⋮ Deformation of Dirac operators along orbits and quantization of noncompact Hamiltonian torus manifolds ⋮ Quantization of Hamiltonian loop group spaces

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Dirac operators on quasi-Hamiltonian \(G\)-spaces
• Elliptic and transversally elliptic index theory from the viewpoint of \(KK\)-theory
• The moment map for circle actions on symplectic manifolds
• Equivariant KK-theory and the Novikov conjecture
• A Bott periodicity theorem for infinite dimensional Euclidean space
• Lie group valued moment maps
• On the spectral characterization of manifolds
• A cubic Dirac operator and the emergence of Euler number multiplets of representations for equal rank subgroups
• Spinor modules for Hamiltonian loop group spaces
• The index of elliptic operators. I
• The index of elliptic operators. III
• Index theory for locally compact noncommutative geometries
• Symplectic reduction and Riemann-Roch formulas for multiplicities
• Loop groups and twisted $K$-theory II
• Basic noncommutative geometry