John Nicholson

I am currently a Heilbronn Research Fellow at Imperial College London. Until October 2021, I was a PhD student at University College London working under the supervision of Francis E. A. Johnson.


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 current focus is on the development of new algebraic techniques to classify finite 2-dimensional cell complexes, i.e. group presentations, up to homotopy equivalence. I also work on applying these techniques to the classification of manifolds and Poincaré complexes in dimensions 3 and 4.

Publications and Preprints

  1. The homotopy type of a finite 2-complex with non-minimal Euler characteristic (August 2021)
    Submitted, 23 pages (arXiv version)

  2. Homotopy classification of 4-manifolds whose fundamental group is dihedral (November 2020)
    with Daniel Kasprowski and Benjamin Ruppik
    Algebraic & Geometric Topology, to appear, 22 pages (arXiv version)

  3. Cancellation for (G,n)-complexes and the Swan finiteness obstruction (May 2020)
    Submitted, 29 pages (arXiv version)

  4. Projective modules and the homotopy classification of (G,n)-complexes (April 2020)
    Submitted, 28 pages (arXiv version)

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

  6. On CW-complexes over groups with periodic cohomology (May 2019)
    Transactions of the American Mathematical Society, 374 (2021), 6531-6557 (journal version, arXiv version)

  7. A cancellation theorem for modules over integral group rings (July 2018)
    Mathematical Proceedings of the Cambridge Philosophical Society, 171 (2021), 317-327 (journal version, arXiv version)


Invited talks Selected Junior/Contributed Talks

Conferences and Workshops


2020-21 2018-19 2017-18


My Part III essay on Exotic Spheres which was supervised by Oscar Randal-Williams.

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.