Abstract: To study knots in $R^3$, it's natural to analyse the combinatorics of their projections to some plane. To generalise this to arbitrary three-manifolds, one can consider projections to spines, two-complexes which play an important role in computational topology. In addition to describing some results about spine projections of isotopic links, I'll explain a connection to an open result about shadows of four-manifolds. The work I'll describe is joint with Brand, Burton, Dancso, He, and Jackson.
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