A note on the theorems of Lusternik-Schnirelmann and Borsuk-Ulam

T. E. Barros; C. Biasi

T. E. Barros ; C. Biasi

Colloquium Mathematicae, Tome 111 (2008), p. 35-42 / Harvested from The Polish Digital Mathematics Library

Résumé

Let p be a prime number and X a simply connected Hausdorff space equipped with a free $ℤ_{p}$ -action generated by $f_{p} : X \to X$ . Let $α : S^{2 n - 1} \to S^{2 n - 1}$ be a homeomorphism generating a free $ℤ_{p}$ -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 $F : (S^{2 n - 1}, α) \to (X, f_{p})$ . As applications, we derive new versions of generalized Lusternik-Schnirelmann and Borsuk-Ulam theorems.

Publié le : 2008-01-01

Zbl 1142.55002

EUDML-ID : urn:eudml:doc:283712

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T. E. Barros; C. Biasi. A note on the theorems of Lusternik-Schnirelmann and Borsuk-Ulam. Colloquium Mathematicae, Tome 111 (2008) pp. 35-42. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm111-1-3/