Alexandra Kjuchukova,"Rep-tiles"

Thursday May 29, 2025, 10:30 AM → 12:00 PM Europe/Paris

An n-dimensional rep-tile X is a compact codimension-zero submanifold of R^n, with the property that it be decomposed as the union of mutually isometric manifolds similar to X which have non-overlapping interiors. For one astonishing example, all knot exteriors are homeomorphic to rep-tiles, by a 2021 result of Blair, Marley and Richards. I will show how to construct new rep-tiles, and I will give an isotopy classification of rep-tiles in all dimensions. In part two, I will outline the main proof, which is based on a technique called equivariant ball swap. Based on joint work with Ryan Blair, Patricia Cahn and Hannah Schwartz (arxiv 2412.19986