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Counterexamples in 4-manifold topology

2023; Volume: 9; Issue: 1 Linguagem: Inglês

10.4171/emss/56

2308-216X

Daniel Kasprowski, Mark Powell, Arunima Ray,

Homotopy and Cohomology in Algebraic Topology

We illustrate the rich landscape of 4-manifold topology through the lens of counterexamples. We consider several of the most commonly studied equivalence relations on 4-manifolds and how they are related to one another. We explain implications e.g. that $h$-cobordant manifolds are stably homeomorphic, and we provide examples illustrating the failure of other potential implications. The information is conveniently organised in a flowchart and a table.