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

• Autorzy: T. E. Barros , C. Biasi
• Języki publikacji: EN

Abstrakty

EN

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

Kategorie tematyczne

• 55M20: Fixed points and coincidences
• 55M35: Finite groups of transformations (including Smith theory)
• 55M30: Ljusternik-Schnirelman (Lyusternik-Shnirel\cprime man) category of a space

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 2008
• Tom: 111
• Numer: 1
• Strony: 35-42

Daty

wydano

2008

Twórcy

autor

T. E. Barros

• DM-UFSCar, CP 676, 13565-905 São Carlos-SP, Brazil

autor

C. Biasi

• ICMC-USP, CP 668, 13560-970 São Carlos-SP, Brazil

Identyfikatory

DOI

10.4064/cm111-1-3