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- W4295962960 abstract "Through the glasses of didactic reduction: We consider a (periodic) tessellation $Delta$ of either Euclidean or hyperbolic $n$-space $M$. By a piecewise isometric rearrangement of $Delta$ we mean the process of cutting $M$ along corank-1 tile-faces into finitely many convex polyhedral pieces, and rearranging the pieces to a new tight covering of the tessellation $Delta$. Such a rearrangement defines a permutation of the (centers of the) tiles of $Delta$, and we are interested in the group $PI(Delta)$ of all piecewise isometric rearrangements of $Delta$. In this paper we offer: a) An illustration of piecewise isometric rearrangements in the visually attractive hyperbolic plane, b) an explanation how this is related to Richard Thompson's groups, c) a chapter on the structure of the group pei$(mathbb Z^n)$ of all piecewise Euclidean rearrangements of the standard tessellation of $mathbb R^n$ by unit-cubes, and d) results on the finiteness properties of some subgroups of pei$(mathbb Z^n)$." @default.
- W4295962960 created "2022-09-16" @default.
- W4295962960 creator A5035856778 @default.
- W4295962960 creator A5046317836 @default.
- W4295962960 date "2021-10-12" @default.
- W4295962960 modified "2023-09-24" @default.
- W4295962960 title "Groups of piecewise isometric permutations of lattice points or finitary rearrangements of tessellations" @default.
- W4295962960 doi "https://doi.org/10.48550/arxiv.2110.05788" @default.
- W4295962960 hasPublicationYear "2021" @default.
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