Tile homotopy groups, computations and examples

Michael Reid

University of Massachusetts Amherst

April 4,
refreshments at 3:45pm


To a finite set of polyomino prototiles, Conway and Lagarias associate a finitely presented group, and they show that the tiling of a region by the protoset implies the vanishing of a certain group element. They also show that the tiling restrictions thus obtained are always as strong as, and may be stronger than any restrictions obtained by generalized checkerboard colorings.

The Conway-Lagarias technique has only been applied successfully in a handful of cases. We present a strategy for applying the technique which is successful in many cases. We also give a number of new examples where we obtain tiling restrictions that cannot be obtained by generalized checkerboard colorings.

We also discuss tiling restrictions that cannot be detected by the tile homotopy group.

Speaker's Contact Info: mreid(at-sign)math.umass.edu

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Combinatorics Seminar, Mathematics Department, MIT, sara(at-sign)math.mit.edu

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