Measuring knotted graph complexity via simplicial complexes

There has been significant interest in simplicial complexes,
such as the curve complex and the pants complex, due to their
applications in the study of mapping class groups of surfaces and
Teichmüller theory. Since low-dimensional manifolds and the knotted
objects within them, can be decomposed into simpler pieces along a
surface S, these complexes on S provide a means of measuring
entanglement complexity. In this talk, we will discuss how we estimate
the complexity of certain families of knotted graphs in 3-manifolds
using distances in the curve and pants complexes. This work is part of
an ongoing collaboration with Puttipong Pongtanapaisan and Sayantika Mondal.