Domination of manifolds by hypersurfaces

TL;DR

This paper proves that every smooth, closed, oriented manifold can be represented as a dominating submanifold of a sphere with codimension one, establishing a universal domination property.

Contribution

It introduces a universal domination result showing all such manifolds can be dominated by hypersurfaces in spheres, a new insight in geometric topology.

Findings

Any smooth, closed, oriented manifold can be dominated by a codimension 1 submanifold of the sphere.

The result applies broadly to all such manifolds, indicating a universal property.

Provides a new perspective on the relationship between manifolds and hypersurfaces in spheres.

Abstract

In this short note we prove that any smooth, closed, oriented manifold can be dominated by a codimension 1 submanifold of the sphere.