Nilspaces, nilmanifolds and their morphisms

Understand

Recent developments in ergodic theory, additive combinatorics, higher order Fourier analysis and number theory give a central role to a class of algebraic structures called nilmanifolds.

• In the present paper we continue a program started by Host and Kra.
• We introduce nilspaces as structures satisfying a variant of the Host-Kra axiom system for parallelepiped structures.
• We give a detailed structural analysis of abstract and compact topological nilspaces.