Multiple disjunction for spaces of Poincare embeddings

TL;DR

This paper establishes multirelative connectivity results for spaces of Poincare embeddings, laying groundwork for understanding smooth embedding spaces and their convergence properties in functor calculus.

Contribution

It introduces new connectivity theorems for Poincare embedding spaces, advancing the theoretical framework for studying smooth embeddings.

Findings

Proves multirelative connectivity for Poincare embeddings

Provides foundational results for smooth embedding convergence

Enhances functor calculus methods in embedding theory

Abstract

We obtain multirelative connectivity statements about spaces of Poincare embeddings, as precursors to analogous statements about spaces of smooth embeddings. The latter are the key to convergence results in the functor calculus approach to spaces of embeddings.