Spin cobordism categories in low dimensions

TL;DR

This paper explores the algebraic structures of Madsen-Tillmann spectra associated with categories of low-dimensional Spin manifolds, specifically in three and four dimensions.

Contribution

It provides initial insights into the complex algebraic structures of these spectra, advancing understanding of low-dimensional Spin cobordism categories.

Findings

Identification of rich algebraic structures in the spectra

Initial exploration of three- and four-dimensional cases

Foundation for future detailed studies

Abstract

The Madsen-Tillmann spectra defined by categories of three- and four-dimensional Spin manifolds have a very rich algebraic structure, whose surface is scratched here.