Counterexamples in 4-manifold topology

Abstract

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.

arXiv comment37 pages, 4 figures, 1 table; in v2, we have made several changes in response to a referee report, including writing a more detailed introduction, adding more details about the surgery exact sequence, uniformising the structure of the subsections describing counterexamples, and adding Proposition 5.6. This is the version published in EMS Surveys

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Cited by in corpus (3)

• Gluck twists on concordant or homotopic spheres
• Stable equivalence relations on 4-manifolds
• Four-manifolds, two-complexes and the quadratic bias invariant