A generalization of the Hopf degree theorem

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https://www.ams.org/journals/proc/2023-151-01/S0002-9939-2022-16218-2/

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https://doi.org/10.1090/proc/16218
 http://hdl.handle.net/11603/30338

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UMBC Mathematics and Statistics Department

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https://orcid.org/0000-0002-2662-6760

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2022-10-07

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journal articles
preprints
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Kvalheim, Matthew. “A Generalization of the Hopf Degree Theorem.” Proceedings of the American Mathematical Society 151, no. 01 (January 2023): 453–54. https://doi.org/10.1090/proc/16218.

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Abstract

The Hopf theorem states that homotopy classes of continuous maps from a closed connected oriented smooth 𝒏-manifold 𝑴 to the 𝒏-sphere are classified by their degree. Such a map is equivalent to a section of the trivial 𝒏-sphere bundle over 𝑴. A generalization of the Hopf theorem is obtained for sections of nontrivial oriented 𝒏-sphere bundles over 𝑴.