On the connectivity of three-dimensional tilings

In this talk, I will discuss domino tilings of three dimensional manifolds. In particular, I will focus on the connected components of the space of tilings of such regions under local moves. Using topological techniques we introduce two parameters of tilings: the flux and the twist. Our main result characterizes when two tilings are connected by local moves in terms of these two parameters. (I will not assume any familiarity with the theory of tilings for the talk.)

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