3 papers
math.AT2026
On Realisability of Twisted Homology
Mark Grant, Michael Jung, Baylee Schutte
We discuss the question of when a homology or cohomology class with twisted integer coefficients of a manifold is realised by a submanifold. While this question is classical in…
math.AT2026
Secondary cohomology operations and sectional category
Mark Grant
We show how secondary cohomology operations in the total space of the fibred join can be used to give lower bounds for the sectional category of a fibration. This suggests a refine…
math.GT2025
Immersed but not embedded homology classes
Diarmuid Crowley, Mark Grant
We provide the first documented examples of immersions of closed oriented manifolds which are not homologous to embeddings, thus answering a question posed by Zhenhua Liu. In these…