Automorphisms of procongruence curve and pants complexes

Boggi, Marco; Funar, Louis

doi:10.1112/topo.12306

Cited by 1 publication

(4 citation statements)

References 54 publications

(216 reference statements)

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“…It is not restrictive to assume that ϒ λ = ϒ(S, P) and that σ is in the image of C(S, υ, P) • . The conclusion then follows from Corollary 7.8 and Theorem 4.9 in [12]. Corollary 7.9 implies, in particular, the claim we made at the beginning of this section: Corollary 7.10.…”

Section: The Complex Of Profinite Symmetric Curvessupporting

confidence: 62%

“…It is clear that we have Z ϒ(S,P) ( T(σ ) k ) = Z ˇ (S,P) ( T(σ ) k ) ∩ ϒ(S, P) and the same holds for the normalizers appearing in the statement of the corollary. But then the conclusion is an immediate consequence of Corollary 7.9 and Corollary 4.11 in [12] (see also Corollary 4.3 in [11]).…”

Section: Hyperelliptic Mapping Class Groups Are Goodmentioning

confidence: 83%

“…of an open subgroup is trivial (cf. (i) of Theorem 4.14 in [12]). This then implies the claim of the theorem for P = ∅.…”

Section: Hyperelliptic Mapping Class Groups Are Goodmentioning

confidence: 91%

“…Another interesting case which is not considered in Theorem 7.13 is when (S, υ, P) is a marked hyperelliptic closed surface of genus 1. In this case, ϒ(S, P) = (S, P) so that, by Theorem 4.14 in [12], we have that Z ϒ(S,P) ( ϒ λ ) is generated by the hyperelliptic involution for P ≤ 2 and is trivial for P > 2.…”

Section: Hyperelliptic Mapping Class Groups Are Goodmentioning

confidence: 97%

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Notes on hyperelliptic mapping class groups

Boggi

2023

Glasgow Math. J.

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Hyperelliptic mapping class groups are defined either as the centralizers of hyperelliptic involutions inside mapping class groups of oriented surfaces of finite type or as the inverse images of these centralizers by the natural epimorphisms between mapping class groups of surfaces with marked points. We study these groups in a systematic way. An application of this theory is a counterexample to the genus $2$ case of a conjecture by Putman and Wieland on virtual linear representations of mapping class groups. In the last section, we study profinite completions of hyperelliptic mapping class groups: we extend the congruence subgroup property to the general class of hyperelliptic mapping class groups introduced above and then determine the centralizers of multitwists and of open subgroups in their profinite completions.

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Section: The Complex Of Profinite Symmetric Curvessupporting

confidence: 62%

Section: Hyperelliptic Mapping Class Groups Are Goodmentioning

confidence: 83%

“…of an open subgroup is trivial (cf. (i) of Theorem 4.14 in [12]). This then implies the claim of the theorem for P = ∅.…”

Section: Hyperelliptic Mapping Class Groups Are Goodmentioning

confidence: 91%

Section: Hyperelliptic Mapping Class Groups Are Goodmentioning

confidence: 97%

See 2 more Smart Citations