Classification of homogeneous functors in manifold calculus

TL;DR

This paper extends the classification of homogeneous functors in manifold calculus to a broader setting, constructing a topological space that classifies such functors based on their values on open balls.

Contribution

It generalizes Weiss's classification of homogeneous functors into topological spaces to a more general simplicial model category setting.

Findings

Constructs a classifying space for homogeneous functors in a simplicial model category.

Extends Weiss's classification result beyond topological spaces.

Provides a framework for understanding homogeneous functors in more abstract categories.

Abstract

For any object A in a simplicial model category M, we construct a topological space \^A which classifies homogeneous functors whose value on k open balls is equivalent to A. This extends a classification result of Weiss for homogeneous functors into topological spaces.