activity
20192026
most citedOn CW-complexes over groups with periodic cohomology

10 citations · 15 across the 8 of their papers we have counts for

collaborators

8 papers

math.GT2026

A survey on mapping class groups of 3-manifolds

Philipp Bader, Rachael Boyd, Giulia Carfora +8

We survey computations and tools concerning the mapping class group of a compact, oriented, connected 3-manifold . We provide a guide to the literature and sketch proofs for var…

math.GT2024

Four-manifolds, two-complexes and the quadratic bias invariant

Ian Hambleton, John Nicholson

Kreck and Schafer produced the first examples of stably diffeomorphic closed smooth 4-manifolds which are not homotopy equivalent. They were constructed by applying the doubling co…

math.GT2024

Generalised doubles and simple homotopy types of high dimensional manifolds

Csaba Nagy, John Nicholson, Mark Powell

We characterise the set of fundamental groups for which there exist -manifolds that are -cobordant (hence homotopy equivalent) but not simple homotopy equivalent, when is…

math.GT2024★ 1 cited

Stable equivalence relations on 4-manifolds

Daniel Kasprowski, John Nicholson, Simona Veselá

Kreck's modified surgery gives an approach to classifying smooth -manifolds up to stable diffeomorphism, i.e. up to connected sum with copies of . In dimension…

math.GT2023

On the universal pairing for 2-complexes

Mikhail Khovanov, Vyacheslav Krushkal, John Nicholson

The universal pairing for manifolds was defined and shown to lack positivity in dimension 4 by Freedman et al. We prove an analogous result for 2-complexes, and also show that the…

math.AT2023

Simple homotopy types of even dimensional manifolds

Csaba Nagy, John Nicholson, Mark Powell

Given a closed -manifold, we consider the set of simple homotopy types of -manifolds within its homotopy type, called its simple homotopy manifold set. We characterise it in…

math.GT2020★ 4 cited

Homotopy classification of 4-manifolds whose fundamental group is dihedral

Daniel Kasprowski, John Nicholson, Benjamin Ruppik

We show that the homotopy type of a finite oriented Poincaré 4-complex is determined by its quadratic 2-type provided its fundamental group is finite and has a dihedral Sylow 2-sub…

math.AT2019★ 10 cited

On CW-complexes over groups with periodic cohomology

John Nicholson

If has -periodic cohomology, then D2 complexes over are determined up to polarised homotopy by their Euler characteristic if and only if has at most two one-dimensio…