Waist of the sphere for maps to manifolds

TL;DR

This paper extends the sphere waist theorem and measure partition lemma to maps targeting manifolds, broadening their applicability in geometric topology.

Contribution

It generalizes key measure partition results from spheres to arbitrary manifolds, advancing the understanding of measure concentration and topological mappings.

Findings

Generalization of the sphere waist theorem to manifold targets

Extension of Borsuk--Ulam type measure partition lemma

Broader applicability of measure concentration results

Abstract

We generalize the sphere waist theorem of Gromov and the Borsuk--Ulam type measure partition lemma of Gromov--Memarian for maps to manifolds.