Geodesic
A note on the theorems of Lusternik–Schnirelmann and Borsuk–Ulam
T. E. Barros 1   ; C. Biasi 2
1 DM-UFSCar, CP 676 13565-905 São Carlos-SP, Brazil
2 ICMC-USP, CP 668 13560-970 São Carlos-SP, Brazil
Colloquium Mathematicum, Tome 111 (2008) no. 1, pp. 35-42 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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Let $p$ be a prime number and $X$ a simply connected Hausdorff space equipped with a free $\mathbb Z_p$-action generated by $f_p:X\rightarrow X$. Let $\alpha:S^{2n-1}\rightarrow S^{2n-1}$ be a homeomorphism generating a free $\mathbb Z_p$-action on the $(2n-1)$-sphere, whose orbit space is some lens space. We prove that, under some homotopy conditions on $X$, there exists an equivariant map $F:(S^{2n-1},\alpha)\rightarrow (X,f_p)$. As applications, we derive new versions of generalized Lusternik–Schnirelmann and Borsuk–Ulam theorems.
DOI : 10.4064/cm111-1-3
Mots-clés : prime number simply connected hausdorff space equipped mathbb p action generated rightarrow alpha n rightarrow n homeomorphism generating mathbb p action n sphere whose orbit space lens space prove under homotopy conditions there exists equivariant map n alpha rightarrow applications derive versions generalized lusternik schnirelmann borsuk ulam theorems

T. E. Barros  1   ; C. Biasi  2

1 DM-UFSCar, CP 676 13565-905 São Carlos-SP, Brazil
2 ICMC-USP, CP 668 13560-970 São Carlos-SP, Brazil 
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T. E. Barros; C. Biasi. A note on the theorems of Lusternik–Schnirelmann and Borsuk–Ulam. Colloquium Mathematicum, Tome 111 (2008) no. 1, pp. 35-42. doi: 10.4064/cm111-1-3

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