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Cubical Pachner moves and bordisms of immersions

Gaku Liu, University of Washington
Wednesday, November 18, 2020 - 3:30pm to 5:00pm
via Zoom

Note: This talk begins with a pre-seminar (aimed at graduate students) at 3:30–4:00. The main talk starts at 4:10.

Join Zoom Meeting:
Meeting ID: 950 2088 4635

Simplicial Pachner moves are elementary moves on piecewise linear manifolds that replace one triangulation of the manifold with another. Cubical Pachner moves are the analogous moves on cubulations, i.e. cubical complexes piecewise linearly homeomorphic to a manifold. Unlike the simplicial case, not all cubulations of a manifold are connected through cubical Pachner moves. Funar gave a conjectured characterization of the equivalence classes of cubulations of a manifold modulo Pachner moves. In this talk we prove this characterization, namely, that the equivalence classes are in bijection with bordisms of codimension 1 immersions in the manifold. Joint work with Karim Adiprasito.