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

T. E. Barros, C. Biasi (2008)

Colloquium Mathematicae

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

Conjugation spaces.

Hausmann, Jean-Claude, Holm, Tara, Puppe, Volker (2005)

Algebraic & Geometric Topology

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