James is studying a bachelor of science at ANU majoring in mathematics and statistics. He hopes to commence honours in algebraic topology in 2017. As a student, he would like to know more about category theory and homological algebra. His interests also include areas of theoretical computer science and AI, in particular Kolmogorov complexity.
Stable homotopy theory and category of spectra
The goals of the project are:
- To define stable homotopy groups and discuss their basic properties
- To define the category of spectra following Adams (1974) and discuss its basic properties
- To prove Brown’s representability theorem and show the one to one correspondence between spectra and cohomology theories
- To develop examples, such as the Eilenberg-Maclane spectra, the suspension spectra and K-theory.