Characterisations of K-theory

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The context of the project is work in non-commutative geometry, which relates to several different areas of pure mathematics and mathematical physics. Specifically, the aim is to develop further an axiomatic approach to K-theory. An axiomatic approach is already established for C*-algebra K-theory. The project will generalise this approach to graded C*-algebras and C*-categories. The results will be of great utility to mathematicians working in the field, as well as answering several natural questions.The general method is extrapolation from existing work, along with techniques developed by the researcher's supervisor and colleagues to deal with other problems. The project relates to the EPSRC research areas of algebra, geometry and topology, mathematical analysis, and mathematical physics.