$\mathbb{A}^1$-contractibility of affine modifications
Résumé
We introduce Koras–Russell fiber bundles over algebraically closed fields of characteristic zero. After a single suspension, this exhibits an infinite family of smooth affine A1-contractible 3-folds. Moreover, we give examples of stably A1-contractible smooth affine 4-folds containing a Brieskorn–Pham surface, and a family of smooth affine 3-folds with a higher-dimensional A1-contractible total space.