Open books in dimension four and above

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Dieter Kotschick, IAS
Fine Hall 314

Open book decompositions exist on all three-manifolds, and have been used extensively, for example to understand contact structures. For four-manifolds open book decompositions are fairly rare, although there is some potential to use them, for example in the analysis of Engel structures. I will discuss the existence of open books on four-manifold, highlighting some unexpected obstructions. This also has implications for dimensions higher than four.