Homology Classes of the Circle Space on Spheres and the Discontinuity of Deformations

DOI10.1515/ANS-2005-0101zbMath1075.58008OpenAlexW2514801229WikidataQ125045955 ScholiaQ125045955MaRDI QIDQ4673336

Long, Yiming, Congyi Zhou

Publication date: 29 April 2005

Published in: Advanced Nonlinear Studies (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1515/ans-2005-0101

zbMATH Keywords

deformation2-spherediscontinuitygeodesic polygoncircle spaceLusternik-Schnirelmann theoremnon-trivial homology class

Mathematics Subject Classification ID

Lyusternik-Shnirel'man category of a space, topological complexity à la Farber, topological robotics (topological aspects) (55M30) Abstract critical point theory (Morse theory, Lyusternik-Shnirel'man theory, etc.) in infinite-dimensional spaces (58E05) Global Riemannian geometry, including pinching (53C20) Variational problems in applications to the theory of geodesics (problems in one independent variable) (58E10)

Cites Work

• A nonparametric proof of the theorem of Lusternik and Schnirelman
• Shortening embedded curves

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