Dr John Nicholson
- Rankin-Sneddon Research Fellowship in Pure Mathematics (Mathematics)
email:
John.Nicholson@glasgow.ac.uk
Room 422, Mathematics and Statistics Building, Glasgow, G12 8QS
https://orcid.org/0000-0002-5244-5453Biography
Personal webpage: https://www.maths.gla.ac.uk/~jnicholson/
Research interests
Algebraic and geometric topology, as well as their interactions with areas of algebra such as group theory and integral representation theory.
Research groups
Publications
2025
Kasprowski, Daniel, Nicholson, John 
ORCID: https://orcid.org/0000-0002-5244-5453 and Veselá, Simona
(2025)
Stable equivalence relations on 4-manifolds.
Proceedings of the London Mathematical Society,
(Accepted for Publication)
Khovanov, Mikhail, Krushkal, Vyacheslav and Nicholson, John ORCID: https://orcid.org/0000-0002-5244-5453
(2025)
On the universal pairing for 2‐complexes.
Bulletin of the London Mathematical Society,
(doi: 10.1112/blms.70130)
(Early Online Publication)
Hambleton, Ian and Nicholson, John ORCID: https://orcid.org/0000-0002-5244-5453
(2025)
Four-manifolds, two-complexes and the quadratic bias invariant.
arXiv,
(doi: 10.48550/arXiv.2412.15089)
2024
Nicholson, John ORCID: https://orcid.org/0000-0002-5244-5453
(2024)
The cancellation property for projective modules over integral group rings.
arXiv,
(doi: 10.48550/arXiv.2406.08692)
Nicholson, John ORCID: https://orcid.org/0000-0002-5244-5453
(2024)
Cancellation for (G,n)-complexes and the Swan finiteness obstruction.
International Mathematics Research Notices, 2024(16),
pp. 11832-11864.
(doi: 10.1093/imrn/rnae141)
Nagy, Csaba, Nicholson, John ORCID: https://orcid.org/0000-0002-5244-5453 and Powell, Mark ORCID: https://orcid.org/0000-0002-4086-8758
(2024)
Simple homotopy types of even dimensional manifolds.
arXiv,
(doi: 10.48550/arXiv.2312.00322)
Nicholson, John ORCID: https://orcid.org/0000-0002-5244-5453
(2024)
Projective modules and the homotopy classification of (G,n)-complexes.
Algebraic and Geometric Topology, 24(4),
pp. 2245-2284.
(doi: 10.2140/agt.2024.24.2245)
Kasprowski, Daniel, Nicholson, John ORCID: https://orcid.org/0000-0002-5244-5453 and Veselá, Simona
(2024)
Stable equivalence relations on 4-manifolds.
arXiv,
(doi: 10.48550/arXiv.2405.06637)
2023
Nicholson, John ORCID: https://orcid.org/0000-0002-5244-5453
(2023)
Stably free modules and the unstable classification of 2-complexes.
arXiv,
(doi: 10.48550/arXiv.2108.02220)
2021
Nicholson, John ORCID: https://orcid.org/0000-0002-5244-5453
(2021)
A cancellation theorem for modules over integral group rings.
Mathematical Proceedings of the Cambridge Philosophical Society, 171(2),
pp. 317-327.
(doi: 10.1017/S0305004120000237)
Nicholson, John ORCID: https://orcid.org/0000-0002-5244-5453
(2021)
On CW-complexes over groups with periodic cohomology.
Transactions of the American Mathematical Society, 374(9),
pp. 6531-6557.
(doi: 10.1090/tran/8411)
Articles
Kasprowski, Daniel, Nicholson, John ORCID: https://orcid.org/0000-0002-5244-5453 and Veselá, Simona
(2025)
Stable equivalence relations on 4-manifolds.
Proceedings of the London Mathematical Society,
(Accepted for Publication)
Khovanov, Mikhail, Krushkal, Vyacheslav and Nicholson, John ORCID: https://orcid.org/0000-0002-5244-5453
(2025)
On the universal pairing for 2‐complexes.
Bulletin of the London Mathematical Society,
(doi: 10.1112/blms.70130)
(Early Online Publication)
Hambleton, Ian and Nicholson, John ORCID: https://orcid.org/0000-0002-5244-5453
(2025)
Four-manifolds, two-complexes and the quadratic bias invariant.
arXiv,
(doi: 10.48550/arXiv.2412.15089)
Nicholson, John ORCID: https://orcid.org/0000-0002-5244-5453
(2024)
The cancellation property for projective modules over integral group rings.
arXiv,
(doi: 10.48550/arXiv.2406.08692)
Nicholson, John ORCID: https://orcid.org/0000-0002-5244-5453
(2024)
Cancellation for (G,n)-complexes and the Swan finiteness obstruction.
International Mathematics Research Notices, 2024(16),
pp. 11832-11864.
(doi: 10.1093/imrn/rnae141)
Nagy, Csaba, Nicholson, John ORCID: https://orcid.org/0000-0002-5244-5453 and Powell, Mark ORCID: https://orcid.org/0000-0002-4086-8758
(2024)
Simple homotopy types of even dimensional manifolds.
arXiv,
(doi: 10.48550/arXiv.2312.00322)
Nicholson, John ORCID: https://orcid.org/0000-0002-5244-5453
(2024)
Projective modules and the homotopy classification of (G,n)-complexes.
Algebraic and Geometric Topology, 24(4),
pp. 2245-2284.
(doi: 10.2140/agt.2024.24.2245)
Kasprowski, Daniel, Nicholson, John ORCID: https://orcid.org/0000-0002-5244-5453 and Veselá, Simona
(2024)
Stable equivalence relations on 4-manifolds.
arXiv,
(doi: 10.48550/arXiv.2405.06637)
Nicholson, John ORCID: https://orcid.org/0000-0002-5244-5453
(2023)
Stably free modules and the unstable classification of 2-complexes.
arXiv,
(doi: 10.48550/arXiv.2108.02220)
Nicholson, John ORCID: https://orcid.org/0000-0002-5244-5453
(2021)
A cancellation theorem for modules over integral group rings.
Mathematical Proceedings of the Cambridge Philosophical Society, 171(2),
pp. 317-327.
(doi: 10.1017/S0305004120000237)
Nicholson, John ORCID: https://orcid.org/0000-0002-5244-5453
(2021)
On CW-complexes over groups with periodic cohomology.
Transactions of the American Mathematical Society, 374(9),
pp. 6531-6557.
(doi: 10.1090/tran/8411)
