On the infinite loop space structure of the cobordism category

TL;DR

This paper establishes an equivalence between the classifying space of the cobordism category, with its infinite loop space structure, and the infinite loop space derived from the Madsen-Tillmann spectrum, linking geometric and spectral perspectives.

Contribution

It proves an equivalence of infinite loop spaces connecting the cobordism category's classifying space with the Madsen-Tillmann spectrum, advancing understanding of their topological structures.

Findings

Equivalence of infinite loop spaces established

Classifying space of cobordism category linked to Madsen-Tillmann spectrum

Supports the geometric-spectral connection in topology

Abstract

We show an equivalence of infinite loop spaces between the classify- ing space of the cobordism category, with infinite loop space structure induced by taking disjoint union of manifolds, and the infinite loop space associated to the Madsen-Tillmann spectrum.