A 𝐾-theoretic proof of the Morse index theorem in semi-Riemannian geometry

DOI10.1090/S0002-9939-2011-10874-8zbMath1241.58010arXiv1007.1190OpenAlexW2964068989WikidataQ115289266 ScholiaQ115289266MaRDI QIDQ5388811

Nils Waterstraat

Publication date: 20 April 2012

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1007.1190

zbMATH Keywords

geodesicssemi-Riemannian manifoldsMorse index theorem\(K\)-theroy

Mathematics Subject Classification ID

Particular ordinary differential operators (Dirac, one-dimensional Schrödinger, etc.) (34L40) Index theory and related fixed-point theorems on manifolds (58J20) Geodesics in global differential geometry (53C22) Variational problems in applications to the theory of geodesics (problems in one independent variable) (58E10) Spectral flows (58J30)

Related Items (9)

The Maslov index in weak symplectic functional analysis ⋮ Spectral flow, crossing forms and homoclinics of Hamiltonian systems ⋮ Index theorems for graph-parametrized optimal control problems ⋮ On the Fredholm Lagrangian Grassmannian, spectral flow and ODEs in Hilbert spaces ⋮ Yet another proof of the Morse index theorem ⋮ Jacobi fields in optimal control: Morse and Maslov indices ⋮ The Maslov Index in Symplectic Banach Spaces ⋮ A Morse-Smale index theorem for indefinite elliptic systems and bifurcation ⋮ A family index theorem for periodic Hamiltonian systems and bifurcation

Cites Work

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• Spectral flow and bifurcation of critical points of strongly-indefinite functionals. I: General theory
• Conjugate points on spacelike geodesics or pseudo-self-adjoint Morse-Sturm-Liouville systems
• The Morse index theorem in semi-Riemannian geometry
• A Morse index theorem for perturbed geodesics on semi-Riemannian manifolds
• Morse Theory. (AM-51)
• Spectral asymmetry and Riemannian geometry. III
• The Spectral Flow and the Maslov Index

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