Final Report Summary - RIGIDITY (Rigidity: Groups, Geometry and Cohomology)
The project "Rigidity" has led to new discoveries in pure mathematics. In particular, new paradoxical decompositions have been discovered, and others have been rules out. Paradoxical decompositions are a form of surprising "miraculous" duplication of objects which occur in geometry.
Many geometric discoveries have been made with the help of "groups" -- the algebraic structure that describes the symmetries of objects, of spaces, of graphs, and of more abstract objects.
Many geometric discoveries have been made with the help of "groups" -- the algebraic structure that describes the symmetries of objects, of spaces, of graphs, and of more abstract objects.