3 papers
math.AT2026
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.GT2025
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.GT2025
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…