Tight Embeddings of Simply Connected $4$-Manifolds

The classification of compact and simply connected PL 4-manifolds states that the homeomorphism classes coincide with the homotopy classes, and that these are classified by the intersection form. We show here that ``most'' of these classes with an indefinite intersection form can be represented by a tight polyhedral embedding into some Euclidean space. It remains open which of the PL structures can be realized in such a way.

2000 Mathematics Subject Classification: 52B70, 53C42, 57Q35

Keywords and Phrases: intersection form, tight polyhedra, polyhedral handles, tight surgery

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