Superconnections and higher index theory

DOI10.1007/BF01896662zbMath0777.58038MaRDI QIDQ2366290

John Lott

Publication date: 29 June 1993

Published in: Geometric and Functional Analysis. GAFA (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/58156

zbMATH Keywords

heat equationhyperbolic groupsspin manifoldNovikov conjecturehigher index theory

Mathematics Subject Classification ID

Heat and other parabolic equation methods for PDEs on manifolds (58J35)

Related Items (18)

Equivariant bivariant cyclic theory and equivariant Chern-Connes character ⋮ A note on the higher Atiyah-Patodi-Singer index theorem on Galois coverings ⋮ Noncommutative geometry and conformal geometry. II: Connes-Chern character and the local equivariant index theorem ⋮ Realizing the analytic surgery group of Higson and Roe geometrically. III: Higher invariants ⋮ Rho-classes, index theory and Stolz’ positive scalar curvature sequence ⋮ Dirac index classes and the noncommutative spectral flow ⋮ Relative torsion and bordism classes of positive scalar curvature metrics on manifolds with boundary ⋮ Codimension 2 transfer of higher index invariants ⋮ Delocalized \(L^2\)-invariants ⋮ Twisted Donaldson invariants ⋮ Higher eta-invariants ⋮ Elliptic operators and higher signatures. ⋮ Bivariant Chern character and longitudinal index ⋮ Local index theory over foliation groupoids ⋮ Homotopy invariance of twisted higher signatures on manifolds with boundary ⋮ L²-RHO FORM FOR NORMAL COVERINGS OF FIBER BUNDLES ⋮ Two-cocycle twists and Atiyah–Patodi–Singer index theory ⋮ The $b$-pseudodifferential calculus on Galois coverings and a higher Atiyah-Patodi-Singer index theorem

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Pseudodifferential operators on supermanifolds and the Atiyah-Singer index theorem
• Superconnections and the Chern character
• The Atiyah-Singer index theorem for families of Dirac operators: Two heat equation proofs
• The cyclic homology of the group rings
• Equivariant KK-theory and the Novikov conjecture
• Quantum K-theory. I: The Chern character
• Entire cyclic cohomology of Banach algebras and characters of \(\theta\)- summable Fredholm modules
• The analysis of elliptic families. II: Dirac operators, êta invariants, and the holonomy theorem
• Finite propagation speed, kernel estimates for functions of the Laplace operator, and the geometry of complete Riemannian manifolds
• Sur les groupes hyperboliques d'après Mikhael Gromov. (On the hyperbolic groups à la M. Gromov)
• On the Chern character of a theta-summable Fredholm module
• Cyclic cohomology, the Novikov conjecture and hyperbolic groups
• The index of elliptic operators. III
• The index of elliptic operators. IV, V
• Novikov's higher signature and families of elliptic operators
• Principe d'Oka, K-théorie et systèmes dynamiques non commutatifs. (Oka's principle, K-theory and noncommutative dynamical systems)
• Rational homotopy theory and differential forms

This page was built for publication: Superconnections and higher index theory