Homeomorphisms of a solenoid isotopic to the identity and its second cohomology groups

Reveles-Gurrola, Fermín Omar

Comptes Rendus. Mathématique, Tome 354 (2016) no. 9, pp. 879-886.

Certains aspects de l'étude du groupe d'homéomorphismes d'un solénoïde à une dimension qui sont isotopes à l'identité sont abordés dans la présente contribution. Son sous-groupe maximal, sauf classe d'équivalence homotopique, est décrit, et la classe d'Euler de l'extension centrale universelle de ce groupe est calculée. Cette classe, étant limitée, nous donne une interprétation de l'élément de rotation dans le solénoïde.

Some aspects of the study of the group of homeomorphisms of a one-dimensional solenoid which are isotopic to the identity are discussed in this paper. The maximal subgroup up to homotopy equivalence is described and the Euler class of the universal central extension of this group is calculated. This class being bounded gives an interpretation of the rotation element on the solenoid.

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