Groupes de Cremona, connexit\'e et simplicit\'e
J\'er\'emy Blanc
TL;DR
This paper discusses the properties of the Cremona group, establishing its connectivity in all dimensions and its topological simplicity specifically in dimension 2.
Contribution
It proves the Cremona group's connectivity in all dimensions and its topological simplicity in dimension 2, extending known results.
Findings
Cremona group is connected in all dimensions
Cremona group is topologically simple in dimension 2
Results extend understanding of Cremona group's structure
Abstract
The Cremona group is connected in any dimension and, endowed with its topology, it is simple in dimension 2. ----- Le groupe de Cremona est connexe en toute dimension et, muni de sa topologie, il est simple en dimension 2.
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Taxonomy
TopicsHomotopy and Cohomology in Algebraic Topology · Advanced Topics in Algebra · Finite Group Theory Research