Flattening Knotted Surfaces

Eva Horvat (University of Ljubljana)

A knotted surface \mathcal{K} in the 4-sphere admits a projection to a 2-sphere, whose set of critical points coincides with a hyperbolic diagram of \mathcal{K}. We apply such projections, called flattenings, to define three invariants of embedded surfaces: the width, the trunk and the partition number. These invariants are studied for some families of embedded surfaces.

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