Signature for piecewise continuous groups - Archive ouverte HAL Access content directly
Preprints, Working Papers, ... Year :

Signature for piecewise continuous groups


Let $\widehat{\operatorname{PC}^{\bowtie}}$ be the group of bijections from $\mathopen{[} 0,1 \mathclose{[}$ to itself which are continuous outside a finite set. Let $\operatorname{PC}^{\bowtie}$ be its quotient by the subgroup of finitely supported permutations. We show that the Kapoudjian class of $\operatorname{PC}^{\bowtie}$ vanishes. That is, the quotient map $\widehat{\operatorname{PC}^{\bowtie}} \rightarrow \operatorname{PC}^{\bowtie}$ splits modulo the alternating subgroup of even permutations. This is shown by constructing a nonzero group homomorphism, called signature, from $\widehat{\operatorname{PC}^{\bowtie}}$ to $\mathbb Z / 2 \mathbb Z$. Then we use this signature to list normal subgroups of every subgroup $\widehat{G}$ of $\widehat{\operatorname{PC}^{\bowtie}}$ which contains $\mathfrak{S}_{\mathrm{fin}}$ and such that $G$, the projection of $\widehat{G}$ in $\operatorname{PC}^{\bowtie}$, is simple.
Fichier principal
Vignette du fichier
signature_piecewisecontgroups.pdf (347.51 Ko) Télécharger le fichier
Origin : Files produced by the author(s)

Dates and versions

hal-02491103 , version 1 (27-02-2020)


  • HAL Id : hal-02491103 , version 1


Octave Lacourte. Signature for piecewise continuous groups. 2020. ⟨hal-02491103⟩
82 View
27 Download


Gmail Facebook Twitter LinkedIn More