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arXiv · 1512.01933

Families of \mathbb{A}^1-contractible affine threefolds

Adrien Dubouloz·Jean Fasel
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Abstract

We provide families of affine threefolds which are contractible in the unstable $\mathbb A^1$-homotopy category of Morel-Voevodsky and pairwise non-isomorphic, thus answering a question of A. Asok and B. Doran. As a particular case, we show that the Koras-Russell threefolds of the first kind are contractible, extending results of M. Hoyois, A. Krishna and P. A. Ostvaer.

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Adrien Dubouloz, Jean Fasel. 2015-12-07. Families of \mathbb{A}^1-contractible affine threefolds. https://arxiv.org/abs/1512.01933

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