A note on the theorems of Lusternik-Schnirelmann and Borsuk-Ulam
T. E. Barros, C. Biasi (2008)
Colloquium Mathematicae
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Let p be a prime number and X a simply connected Hausdorff space equipped with a free -action generated by . Let be a homeomorphism generating a free -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 . As applications, we derive new versions of generalized Lusternik-Schnirelmann and Borsuk-Ulam theorems.