Hurwitz–Ran spaces
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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.
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.
Originalsprog | Engelsk |
---|---|
Artikelnummer | 84 |
Tidsskrift | Geometriae Dedicata |
Vol/bind | 217 |
Udgave nummer | 5 |
Sider (fra-til) | 1-56 |
ISSN | 0046-5755 |
DOI | |
Status | Udgivet - 2023 |
ID: 370796532