Abstract:
The rational equivariant cohomology of noncontractible loop spaces is calculated for compact space forms. It is also shown how to use these calculations to establish the existence of closed geodesics.
Bibliography: 18 titles.
Keywords:
spaces of closed curves, rational cohomologies, closed geodesics.
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\by I.~A.~Taimanov
\paper The spaces of non-contractible closed curves in compact space forms
\jour Sb. Math.
\yr 2016
\vol 207
\issue 10
\pages 1458--1470
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Linking options:
https://www.mathnet.ru/eng/sm8708
https://doi.org/10.1070/SM8708
https://www.mathnet.ru/eng/sm/v207/i10/p105
This publication is cited in the following 11 articles:
Hui Liu, Yu Chen Wang, “Generic Existence of Infinitely Many Non-contractible Closed Geodesics on Compact Space Forms”, Acta. Math. Sin.-English Ser., 40:7 (2024), 1674
Hui Liu, Jian Wang, Jingzhi Yan, “The growth of the number of periodic orbits for annulus homeomorphisms and non-contractible closed geodesics on Riemannian or FinslerRP2”, Journal of Differential Equations, 357 (2023), 362
Liu S., Wang W., “A Review of the Index Method in Closed Geodesic Problem”, Acta. Math. Sin.-English Ser., 38:1 (2022), 85–96
Duan H.G., Liu H., “The Non-Contractibility of Closed Geodesics on Finsler Double-Struck Capital Rpn”, Acta. Math. Sin.-English Ser., 38:1 (2022), 1–21
Hui Liu, Yuchen Wang, “Multiplicity of non-contractible closed geodesics on Finsler compact space forms”, Calc. Var., 61:6 (2022)
H. Duan, Y. Long, Ch. Zhu, “Index iteration theories for periodic orbits: old and new”, Nonlinear Anal.-Theory Methods Appl., 201:SI (2020), 111999
Wang W., “Two Closed Geodesics on Compact Bumpy Finsler Manifolds”, Asian J. Math., 24:6 (2020), 985–994
H. Liu, “The optimal lower bound estimation of the number of closed geodesics on finsler compact space form s2n+1/gamma”, Calc. Var. Partial Differ. Equ., 58:3 (2019), 107
H. Liu, Y. Long, Y. Xiao, “The existence of two non-contractible closed geodesics on every bumpy Finsler compact space form”, Discrete Contin. Dyn. Syst., 38:8 (2018), 3803–3829
H. Liu, “The Fadell-Rabinowitz index and multiplicity of non-contractible closed geodesics on Finsler $\mathbb{R}P^n$”, J. Differential Equations, 262:3 (2017), 2540–2553
H. Liu, Y. Xiao, “Resonance identity and multiplicity of non-contractible closed geodesics on Finsler $\mathbb{R}P^n$”, Adv. Math., 318 (2017), 158–190
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