A Study of Hairy Ball Theorem associate with Borsuk-Ulam Theorem

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Md Imran Ali
Pravanjan Kumar Rana

Abstract

In this paper we will provide shorter proof of Hairy Ball theorem using a geometric approach and orientation of curve. Using idea from Borsak-Ulam theorem we will provide few many lemmas and application of Hairy ball theorem.

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A Study of Hairy Ball Theorem associate with Borsuk-Ulam Theorem. J. Int. Acad. Phys. Sci. [Internet]. 2025 Jun. 15 [cited 2026 Oct. 23];29(2):55-9. Available from: http://www.iaps.org.in/journal/index.php/journaliaps/article/view/1018

References

M. Eisenberg, R. Guy; A proof of the Hairy Ball theorem, Amer. Math. Monthly, 86 (1979), 571-574.

M. R. Adhikari; Basic Algebraic Topology and its Applications, Springer, 2016.

E. H. Spanier; Algebraic Topology, Mc Graw-Hill, New York.

Algebraic Topolgy: Beckham Mayers lecture notes.

John M. Lee; Introduction to Smooth Manifolds, 2003.

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