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arXiv · 1305.0993

Sofic profile and computability of Cremona groups

Yves Cornulier
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Abstract

In this paper, we show that Cremona groups are sofic. We actually introduce a quantitative notion of soficity, called sofic profile, and show that the group of birational transformations of a d-dimensional variety has sofic profile at most polynomial of degree d. We also observe that finitely generated subgroups of the Cremona group have a solvable word problem. This provides examples of finitely generated groups with no embeddings into any Cremona group, answering a question of S. Cantat.

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Yves Cornulier. 2013-05-05. Sofic profile and computability of Cremona groups. https://doi.org/10.1307/mmj/1387226167

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