Twisted geometry for submanifolds of $\mathbb{R}^n$

Abstract

This is a friendly introduction to our recent general procedure for constructing noncommutative deformations of an embedded submanifold of R determined by a set of smooth equations ( ) = 0. We use the framework of Drinfel'd twist deformation of differential geometry pioneered in [Aschieri et al., Class. Quantum Gravity 23 (2006), 1883]; the commutative pointwise product is replaced by a (generally noncommutative) ★-product induced by a Drinfel'd twist.