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

T. E. Barros, and C. Biasi. "A note on the theorems of Lusternik-Schnirelmann and Borsuk-Ulam." Colloquium Mathematicae 111.1 (2008): 35-42. <http://eudml.org/doc/283712>.

@article{T2008,
abstract = {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.},
author = {T. E. Barros, C. Biasi},
journal = {Colloquium Mathematicae},
keywords = {Borsuk-Ulam theorem; LS category; equivariant map},
language = {eng},
number = {1},
pages = {35-42},
title = {A note on the theorems of Lusternik-Schnirelmann and Borsuk-Ulam},
url = {http://eudml.org/doc/283712},
volume = {111},
year = {2008},
}

TY - JOUR
AU - T. E. Barros
AU - C. Biasi
TI - A note on the theorems of Lusternik-Schnirelmann and Borsuk-Ulam
JO - Colloquium Mathematicae
PY - 2008
VL - 111
IS - 1
SP - 35
EP - 42
AB - 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.
LA - eng
KW - Borsuk-Ulam theorem; LS category; equivariant map
UR - http://eudml.org/doc/283712
ER -