Naive ${\mathbb{A}}^1$-connectedness of retract rational varieties

Abstract

A smooth, proper, retract rational variety over a field $k$ is known to be ${\mathbb{A}}^1$-connected. We improve on this result, in the case when $k$ is infinite, showing that such varieties are naively ${\mathbb{A}}^1$-connected.

14 pages, comments are welcome