Hurwitz–Ran spaces

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Hurwitz–Ran spaces. / Bianchi, Andrea.

I: Geometriae Dedicata, Bind 217, Nr. 5, 84, 2023, s. 1-56.

Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › fagfællebedømt

Harvard

Bianchi, A 2023, 'Hurwitz–Ran spaces', Geometriae Dedicata, bind 217, nr. 5, 84, s. 1-56. https://doi.org/10.1007/s10711-023-00820-z

APA

Bianchi, A. (2023). Hurwitz–Ran spaces. Geometriae Dedicata, 217(5), 1-56. [84]. https://doi.org/10.1007/s10711-023-00820-z

Vancouver

Bianchi A. Hurwitz–Ran spaces. Geometriae Dedicata. 2023;217(5):1-56. 84. https://doi.org/10.1007/s10711-023-00820-z

Author

Bianchi, Andrea. / Hurwitz–Ran spaces. I: Geometriae Dedicata. 2023 ; Bind 217, Nr. 5. s. 1-56.

Bibtex

@article{4186b7a7e0ed4cd8846de1926be76217,
title = "Hurwitz–Ran spaces",
abstract = "Given a couple of subspaces of the complex plane satisfying some mild conditions (a “nice couple”), and given a PMQ-pair , consisting of a partially multiplicative quandle (PMQ) and a group G, we introduce a “Hurwitz–Ran” space , containing configurations of points in and in with monodromies in and in G, respectively. We further introduce a notion of morphisms between nice couples, and prove that Hurwitz–Ran spaces are functorial both in the nice couple and in the PMQ-group pair. For a locally finite PMQ we prove a homeomorphism between and the simplicial Hurwitz space , introduced in previous work of the author: this provides in particular with a cell stratification in the spirit of Fox–Neuwirth and Fuchs.",
author = "Andrea Bianchi",
year = "2023",
doi = "10.1007/s10711-023-00820-z",
language = "English",
volume = "217",
pages = "1--56",
journal = "Geometriae Dedicata",
issn = "0046-5755",
publisher = "Springer",
number = "5",

}

RIS

TY - JOUR

T1 - Hurwitz–Ran spaces

AU - Bianchi, Andrea

PY - 2023

Y1 - 2023

N2 - Given a couple of subspaces of the complex plane satisfying some mild conditions (a “nice couple”), and given a PMQ-pair , consisting of a partially multiplicative quandle (PMQ) and a group G, we introduce a “Hurwitz–Ran” space , containing configurations of points in and in with monodromies in and in G, respectively. We further introduce a notion of morphisms between nice couples, and prove that Hurwitz–Ran spaces are functorial both in the nice couple and in the PMQ-group pair. For a locally finite PMQ we prove a homeomorphism between and the simplicial Hurwitz space , introduced in previous work of the author: this provides in particular with a cell stratification in the spirit of Fox–Neuwirth and Fuchs.

AB - Given a couple of subspaces of the complex plane satisfying some mild conditions (a “nice couple”), and given a PMQ-pair , consisting of a partially multiplicative quandle (PMQ) and a group G, we introduce a “Hurwitz–Ran” space , containing configurations of points in and in with monodromies in and in G, respectively. We further introduce a notion of morphisms between nice couples, and prove that Hurwitz–Ran spaces are functorial both in the nice couple and in the PMQ-group pair. For a locally finite PMQ we prove a homeomorphism between and the simplicial Hurwitz space , introduced in previous work of the author: this provides in particular with a cell stratification in the spirit of Fox–Neuwirth and Fuchs.

U2 - 10.1007/s10711-023-00820-z

DO - 10.1007/s10711-023-00820-z

M3 - Journal article

VL - 217

SP - 1

EP - 56

JO - Geometriae Dedicata

JF - Geometriae Dedicata

SN - 0046-5755

IS - 5

M1 - 84

ER -

ID: 370796532