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- W3207252893 abstract "Through the glasses of didactic reduction, we consider a (periodic) tessellation Δ $Delta$ of either Euclidean or hyperbolic n $n$ -space M $M$ . By a piecewise isometric rearrangement of Δ $Delta$ we mean the process of cutting M $M$ along corank-1 tile-faces into finitely many convex polyhedral pieces, and rearranging the pieces to a new tight covering of the tessellation Δ $Delta$ . Such a rearrangement defines a permutation of the (centers of the) tiles of Δ $Delta$ , and we are interested in the group P I ( Δ ) $PI(Delta )$ of all piecewise isometric rearrangements of Δ $Delta$ . In this paper, we offer (a) an illustration of piecewise isometric rearrangements in the visually attractive hyperbolic plane, (b) an explanation on how this is related to Richard Thompson's groups, (c) a section on the structure of the group pei ( Z n ) $(mathbb {Z}^n)$ of all piecewise Euclidean rearrangements of the standard cubically tessellated R n $mathbb {R}^n$ , and (d) results on the finiteness properties of some subgroups of pei ( Z n ) $(mathbb {Z}^n)$ ." @default.
- W3207252893 created "2021-10-25" @default.
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- W3207252893 date "2022-09-14" @default.
- W3207252893 modified "2023-09-26" @default.
- W3207252893 title "Groups of piecewise isometric permutations of lattice points, or Finitary rearrangements of tessellations" @default.
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- W3207252893 doi "https://doi.org/10.1112/jlms.12503" @default.
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