The rational homotopy theory of certain path spaces with applications to geodesics

DOI10.1007/BF02392310zbMath0421.58007MaRDI QIDQ1133218

Micheline Vigué-Poirrier, Stephen Halperin, Karsten Grove

Publication date: 1978

Published in: Acta Mathematica (Search for Journal in Brave)

zbMATH Keywords

rational homotopy theorygeodesicsminimal modelsloop space of the complete Riemannian manifold

Mathematics Subject Classification ID

Rational homotopy theory (55P62) Variational problems in applications to the theory of geodesics (problems in one independent variable) (58E10)

Related Items (15)

Rational homotopy of the (homotopy) fixed point sets of circle actions ⋮ Metrics with only finitely many isometry invariant geodesics ⋮ Isometry-invariant geodesics on spheres ⋮ Homology of primitive quotients of the universal enveloping algebra of \({\mathfrak sl}(2)\) ⋮ On the number of invariant closed geodesics ⋮ Homotopie rationnelle et croissance du nombre de géodésiques fermées ⋮ Homotopie rationnelle et croissance du nombre de géodésiques fermées ⋮ Splitting lemmas for the Finsler energy functional on the space ofH¹-curves ⋮ Dans le fibre de l'espace des lacets libres, la fibre n'est pas, en général, totalement non cohomologue à zéro ⋮ Contributions of rational homotopy theory to global problems in geometry ⋮ Equivariant rational homotopy theory as a closed model category ⋮ Elliptic isometries, condition (C) and proper maps ⋮ The cohomology of a pull-back on \({\mathbb K}\)-formal spaces ⋮ On the Betti number of the space of invariant paths on the space whose cohomology is the exterior algebra with two generators ⋮ Rigidity properties of compact Lie groups modulo maximal tori

Cites Work

• Geodesics satisfying general boundary conditions
• The geometric realization of a semi-simplicial complex
• Real homotopy theory of Kähler manifolds
• The homology theory of the closed geodesic problem
• Infinitesimal computations in topology
• Obstructions to homotopy equivalences
• Condition (C) for the energy integral on certain path spaces and applications to the theory of geodesics
• Isometry-invariant geodesics
• Periodic geodesics on compact Riemannian manifolds
• Tarski's definition of point in Banach spaces
• On the number of invariant closed geodesics
• Finiteness in the Minimal Models of Sullivan
• Rational Fibrations, Minimal Models, and Fibrings of Homogeneous Spaces
• Unnamed Item

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