Characterisations of K-theory

该项目的背景是非对易几何方面的工作，这涉及到纯数学和数学物理的几个不同领域。具体地说，其目的是进一步发展K-理论的公理方法。对于C*-代数K-理论，已经建立了一种公理方法。该项目将把这种方法推广到分次C*-代数和C*-范畴。这些结果将对在该领域工作的数学家以及回答几个自然问题非常有用。通常的方法是从现有的工作中推断，以及研究人员的主管和同事开发的处理其他问题的技术。该项目涉及EPSRC的代数、几何和拓扑学、数学分析和数学物理等研究领域。

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.