Embedding, compression, and the relative Hopf invariant

TL;DR

This paper extends Poincaré embedding results to the relative setting and introduces a new equivariant relative Hopf invariant, with applications to non-simply connected Poincaré surgery.

Contribution

It generalizes Poincaré embedding results to the relative case and introduces the relative Hopf invariant in the equivariant setting.

Findings

Established relative Poincaré embedding results

Introduced the equivariant relative Hopf invariant

Laid groundwork for applications in Poincaré surgery

Abstract

We establish Poincar\'e embedding results in the relative setting, generalizing previously known results in the absolute case. Our primary motivation comes from applications to non-simply connected Poincar\'e surgery, which will be developed in a forthcoming paper. Along the way, we introduce a new tool: the relative Hopf invariant in the equivariant setting.