# On the classifying spaces of cobordisms of singular maps

## TL;DR

This paper explores two different constructions of classifying spaces for cobordisms of singular maps, establishing a homotopy connection and revealing cases with simple product structures.

## Contribution

It uncovers a homotopy theoretical link between two constructions and identifies conditions under which classifying spaces have a straightforward product form.

## Key findings

- Established a homotopy connection between two classifying space constructions.
- Identified cases where classifying spaces have a simple product structure.
- Enhanced understanding of the topology of cobordism classifying spaces.

## Abstract

The classifying spaces of cobordisms of singular maps have two fairly different constructions. We expose a homotopy theoretical connection between them. As a corollary we show that the classifying spaces in some cases have a simple product structure.