# What's that space?

A major problem arising in modern mathematics is determining whether two objects or spaces are the same.

There are various notions of "sameness" that can be used, but we investigate whether spaces are topologically equivalent, i.e. if one space can be deformed into another. Algebraic topology is about associating computable algebraic invariants to spaces which helps to determine whether they are topologically equivalent.

One such invariant is topological K-theory, which measures how many different types of vector bundles there are over a space. There are various modified versions of K-theory, such as higher twisted K-theory, which is the subject of my research. The aims of this project are to explicitly calculate the higher twisted K-theory of various spaces, investigate the algebraic structure of higher twisted K-theory, and to geometrically describe the higher twists of K-theory.

**Theme**

Transforming technologies

**Booth**

TT29

**School**

Mathematical Sciences

**Exhibitor**

David Leonard Brook