Geodesic
A note on the theorems of Lusternik–Schnirelmann and Borsuk–Ulam
T. E. Barros1 ; C. Biasi2
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.

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

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 
@article{10_4064_cm111_1_3,
     author = {T. E. Barros and C. Biasi},
     title = {A note on the theorems of {Lusternik{\textendash}Schnirelmann} and {Borsuk{\textendash}Ulam}},
     journal = {Colloquium Mathematicum},
     pages = {35--42},
     publisher = {mathdoc},
     volume = {111},
     number = {1},
     year = {2008},
     doi = {10.4064/cm111-1-3},
     language = {de},
     url = {http://geodesic.mathdoc.fr/articles/10.4064/cm111-1-3/}
}
TY  - JOUR
AU  - T. E. Barros
AU  - C. Biasi
TI  - A note on the theorems of Lusternik–Schnirelmann and Borsuk–Ulam
JO  - Colloquium Mathematicum
PY  - 2008
SP  - 35
EP  - 42
VL  - 111
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.4064/cm111-1-3/
DO  - 10.4064/cm111-1-3
LA  - de
ID  - 10_4064_cm111_1_3
ER  - 
%0 Journal Article
%A T. E. Barros
%A C. Biasi
%T A note on the theorems of Lusternik–Schnirelmann and Borsuk–Ulam
%J Colloquium Mathematicum
%D 2008
%P 35-42
%V 111
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.4064/cm111-1-3/
%R 10.4064/cm111-1-3
%G de
%F 10_4064_cm111_1_3
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. http://geodesic.mathdoc.fr/articles/10.4064/cm111-1-3/

Cité par Sources :