Topological Colored Tverberg Theorem and the Reduction Lemma

TL;DR

This paper provides a proof of the BMZ Reduction Lemma with a motivational perspective and extends it to maps into manifolds, offering geometric insights into the colored topological Tverberg theorem.

Contribution

It introduces a new proof of the BMZ Reduction Lemma and extends its application to manifold mappings, enhancing understanding of the colored Tverberg theorem.

Findings

Proof of the BMZ Reduction Lemma with a motivational perspective

Extension of the lemma to maps into manifolds using cohomological dimension

Geometric insights into the colored topological Tverberg theorem

Abstract

In this paper we present a proof of the BMZ Reduction Lemma with a motivational perspective, and state this lemma for maps to manifolds using the classical definition of cohomological dimension. The lemma, proved and utilized in [4], gives a geometrical insight in the proof of the BMZ colored topological Tverberg theorem.