Borsuk-Ulam theorem, fixed point index and chain approximations for maps with multiplicity

Fritz von Haeseler and Guentcho Svetoslavov Skordev

Vol. 153 (1992), No. 2, 369–396

DOI: 10.2140/pjm.1992.153.369

Abstract

In this article we consider m-acyclic maps with respect to a field 𝔽 and prove the existence of chain approximation for such maps. Furthermore we provide a unified approach to the Borsuk-Ulam theorem and the Bourgin-Yang generalization. Finally we prove the existence of A-systems for certain m-acyclic maps and define a fixed point index.

Mathematical Subject Classification 2000

Primary: 55M20

Milestones

Received: 13 March 1990

Published: 1 April 1992