AF-algebras and topology of mapping tori

TL;DR

This paper constructs a functor linking mapping tori to AF-algebras and uses it to develop an obstruction theory for low-dimensional torus bundles, advancing the understanding of their topological and algebraic structures.

Contribution

It introduces a covariant functor from mapping tori to AF-algebras and applies it to create an obstruction theory for 2, 3, and 4-dimensional torus bundles.

Findings

Established a functor from mapping tori to AF-algebras

Developed an obstruction theory for low-dimensional torus bundles

Connected topological properties with algebraic invariants

Abstract

A covariant functor from the category of mapping tori to a category of AF-algebras is constructed; the functor takes continuous maps between such manifolds to stable homomorphisms between the corresponding AF-algebras. We use this functor to develop an obstruction theory for the torus bundles of dimension 2, 3 and 4.