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

TL;DR

This paper proves that smooth, proper, retract rational varieties over infinite fields are naively $ ext{A}^1$-connected, strengthening previous results about their $ ext{A}^1$-connectedness.

Contribution

It establishes the naive $ ext{A}^1$-connectedness of retract rational varieties over infinite fields, improving upon known $ ext{A}^1$-connectedness results.

Findings

Retract rational varieties are naively $ ext{A}^1$-connected over infinite fields.

Strengthens previous $ ext{A}^1$-connectedness results.

Applicable to smooth, proper varieties over infinite fields.

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.