Determination of compact Lie groups with the Borsuk-Ulam property
Abstract
In this paper, we shall discuss the classical question of which compact Lie groups have the Borsuk-Ulam property and in particular we shall show that every extension group of a n-torus by a cyclic group of prime order does not have the Borsuk-Ulam property. This leads us that the only compact Lie groups with the Borsuk-Ulam property are an elementary abelian p-group and an n-torus, which is a final answer to the question.
- Publication:
-
arXiv e-prints
- Pub Date:
- July 2021
- DOI:
- 10.48550/arXiv.2107.13158
- arXiv:
- arXiv:2107.13158
- Bibcode:
- 2021arXiv210713158N
- Keywords:
-
- Mathematics - Algebraic Topology;
- 55M20;
- 55S35