Geodesic
Signature for piecewise continuous groups
Octave Lacourte1
1Université Claude Bernard Lyon 1, Villeurbanne, France
Groups, geometry, and dynamics, Tome 16 (2022) no. 1, pp. 75-84

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DOI

Let PC⋈ be the group of bijections from [0,1[ to itself which are continuous outside a finite set. Let PC⋈ be its quotient by the subgroup of finitely supported permutations. We show that the Kapoudjian class of PC⋈ vanishes. That is, the quotient map PC⋈→PC⋈ splits modulo the alternating subgroup of even permutations. This is shown by constructing a nonzero group homomorphism, called signature, from PC⋈ to Z/2Z. Then we use this signature to list normal subgroups of every subgroup G of PC⋈ which contains Sfin​ such that G, the projection of G in PC⋈, is simple.
DOI : 10.4171/ggd/664
Classification : 37-XX, 20-XX
Mots-clés : Permutations groups, interval exchange transformations, signature, Kapoudjian class

Octave Lacourte  1

1 Université Claude Bernard Lyon 1, Villeurbanne, France 
Octave Lacourte. Signature for piecewise continuous groups. Groups, geometry, and dynamics, Tome 16 (2022) no. 1, pp. 75-84. doi: 10.4171/ggd/664
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