John Nicholson

I am currently a Rankin-Sneddon Research Fellow at the University of Glasgow. Previously, I was a Heilbronn Research Fellow at Imperial College London. In October 2021, I completed my PhD at University College London under the supervision of F. E. A. Johnson. Before that, I was a student at the University of Cambridge.

I co-organise the Geometry and Topology Seminar at the University of Glasgow.


Research Interests

My research is on classification problems in low-dimensional topology and their interactions with areas of algebra such as homological group theory and integral representation theory. My time is currently split between the following closely-related topics:

Publications and Preprints

  1. On the universal pairing for 2-complexes, with Mikhail Khovanov and Slava Krushkal
    Submitted, 17 pages (arXiv:2312.07429)

  2. Simple homotopy types of even dimensional manifolds, with Csaba Nagy and Mark Powell
    Submitted, 76 pages (arXiv:2312.00322)

  3. Stably free modules and the unstable classification of 2-complexes
    Submitted, 29 pages (arXiv:2108.02220)

  4. Cancellation for (G,n)-complexes and the Swan finiteness obstruction
    Submitted, 29 pages (arXiv:2005.01664)

  1. Projective modules and the homotopy classification of (G,n)-complexes
    Algebraic & Geometric Topology, to appear, 28 pages (arXiv:2004.04252)

  2. Homotopy classification of 4-manifolds whose fundamental group is dihedral, with Daniel Kasprowski and Benjamin Ruppik
    Algebraic & Geometric Topology, 22 (2022), 2915-2949 (journal version, arXiv:2011.03520)

  3. Connected sum decompositions of high-dimensional manifolds, with Imre Bokor, Diarmuid Crowley, Stefan Friedl, Fabian Hebestreit, Daniel Kasprowski, Markus Land
    2019-20 MATRIX Annals (2021), 5-30 (journal version, arXiv:1909.02628)

  4. On CW-complexes over groups with periodic cohomology
    Transactions of the American Mathematical Society, 374 (2021), 6531-6557 (journal version, arXiv:1905.12018)

  5. A cancellation theorem for modules over integral group rings
    Mathematical Proceedings of the Cambridge Philosophical Society, 171 (2021), 317-327 (journal version, arXiv:1807.00307)


Invited seminar talks Conference talks

Conferences and Workshops

In person Online


2023-24 2022-23 2020-21 2018-19 2017-18


From April 2019 to 2020, I was a part of the editorial team of Chalkdust.

I am a coauthor of the textbook Edexcel A-level Further Mathematics Core Pure Mathematics Book 2 which was published by Pearson in March 2018.

I am a contributor to the material on the website Underground Mathematics, which I worked on during the summer of 2015.

Here are some instructions on How to Set Up a UCL webpage.