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 1-contractible 3-folds. Moreover, we give examples of stably 1-contractible smooth affine 4-folds containing a Brieskorn-Pham surface, and a family of smooth affine 3-folds with a higher-dimensional 1-contractible total space.
A(1)-contractibility of affine modifications / A. Dubouloz, S. Pauli, P.A. Oestvaer. - In: INTERNATIONAL JOURNAL OF MATHEMATICS. - ISSN 0129-167X. - 30:14(2019), pp. 1950069.1-1950069.34. [10.1142/S0129167X19500691]
A(1)-contractibility of affine modifications
P.A. Oestvaer
2019
Abstract
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 1-contractible 3-folds. Moreover, we give examples of stably 1-contractible smooth affine 4-folds containing a Brieskorn-Pham surface, and a family of smooth affine 3-folds with a higher-dimensional 1-contractible total space.
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