The topological transversal Tverberg theorem plus constraints

TL;DR

This paper develops new topological transversal Tverberg theorems using advanced topological methods, extending classical results with constraints and generalized theorems.

Contribution

It introduces a novel combination of the constraint method with generalized Borsuk-Ulam and cohomological intersection lemmas to derive new transversal Tverberg theorems.

Findings

Derived a topological generalized transversal Van Kampen-Flores theorem.

Established a topological transversal weak colored Tverberg theorem.

Extended classical Tverberg results to transversal and constrained settings.

Abstract

In this paper we use the strength of the constraint method in combination with a generalized Borsuk-Ulam type theorem and a cohomological intersection lemma to show how one can obtain many new topological transversal theorems of Tverberg type. In particular, we derive a topological generalized transversal Van Kampen-Flores theorem and a topological transversal weak colored Tverberg theorem.