# Detecting tightness through open book decompositions

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Andy Wand, University of Glasgow

*Please note the change in time*

We will discuss the notion of consistency' of a self-diffeomorphism of a surface with boundary, and its ability to encode tightness of a contact three-manifold presented as an open book decomposition. Time permitting we will also discuss the relationship of consistency with spectral order', a Floer-theoretic invariant of contact three manifolds defined in joint work with Kutluhan, Matic and Van Horn-Morris.