andrewronan.github.io

Contact Information

Email: ar750@cam.ac.uk

PhD Thesis

• Nilpotent Groups, Spaces and G-Spaces

Miscellaneous Material

• Model structures on topological spaces - First year PhD project.
• Finitely generated nilpotent spaces - A nilpotent space is equivalent to a CW complex with finite skeleta iff its homotopy groups are finitely generated iff its homology groups are finitely generated.
• Simplicial spaces and fibrations - Proof that the realisation of a ‘locally trivial’ map of simplicial spaces is a Hurewicz fibration. As a consequence, we deduce that the orbit map EG to BG is a Hurewicz fibration whenever G is a topological group with a nondegenerate basepoint.

List of papers

• Completion preserves homotopy fibre squares of connected nilpotent spaces - New York J. Math. 30(2024) 502-512
• Localisations and completions of nilpotent G-spaces - Journal of Homotopy and Related Structures 20(2025) 331-364
• The equivariant covering homotopy property - to appear in the Journal of Homotopy and Related Structures.
• A double coset formula for the genus of a nilpotent group
• A criterion for an h-cofibration to be a q-cofibration - Includes a proof that an h-cofibration between q-cofibrant spaces is a q-cofibration. (Work in progress.)