Geodesic
On the Theorems of Borsuk-Ulam and Ljusternik-Schnirelmann-Borsuk
Canadian mathematical bulletin, Tome 27 (1984) no. 2, pp. 192-204

Voir la notice de l'article provenant de la source Cambridge University Press

Let p ≥ 3 be a prime number and m a positive integer, and let S be the sphere S (m-1)(p-1)-1 . Let f:S→S be a map without fixed points and with f p = idS . We show that there exists an h: S→Rm with h(x) ≠ h(f(x)) for all x ∈ S. From this we conclude that there exists a closed cover U 1,..., U 4m of S with U i nf(U i ) = Ø for i = 1,..., 4m. We apply these results to Borsuk-Ulam and Ljusternik-Schnirelmann-Borsuk theorems in the framework of the sectional category and to a problem in asymptotic fixed point theory.
DOI : 10.4153/CMB-1984-029-6
Mots-clés : 55M20, 47H10 
Steinlein, H. On the Theorems of Borsuk-Ulam and Ljusternik-Schnirelmann-Borsuk. Canadian mathematical bulletin, Tome 27 (1984) no. 2, pp. 192-204. doi: 10.4153/CMB-1984-029-6
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