10 kwietnia 2024

Leonardo Ferrari (IMPAN)

Title: Isometries of tessellated rational homology spheres

Abstract: In this talk, we will describe a combinatorial technique to build
geometric manifolds from right-angled polytopes, discuss some topological
and geometric properties of these manifolds, and explain an algorithm for
the computation of their homology groups. We'll then present a faster
algorithm for the detection of rational homology spheres, and discuss
topological obstructions to their isometries. We'll finally present a method
for building hyperbolic rational homology 3-spheres with isometries of given
order, and mention open problems. No previous knowledge of hyperbolic
geometry will be required in this talk.