## Tight embeddings of simply connected $4$-manifolds

### Summary

Summary: 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.

### Mathematics Subject Classification

52B70, 53C42, 57Q35

### Keywords/Phrases

intersection form, tight polyhedra, polyhedral handles, tight surgery