The Asymptotic Statistics of Random Covering Surfaces
Let $\Gamma _{g}$ be the fundamental group of a closed connected orientable surface of genus $g\geq 2$ . We develop a new method for integrating over the representation space $\mathbb {X}_{g,n}=\mathrm {Hom}(\Gamma _{g},S_{n})$ , where $S_{n}$ is the symmetric group of perm...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Cambridge University Press
2023-01-01
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| Series: | Forum of Mathematics, Pi |
| Subjects: | |
| Online Access: | https://www.cambridge.org/core/product/identifier/S2050508623000136/type/journal_article |
| Summary: | Let
$\Gamma _{g}$
be the fundamental group of a closed connected orientable surface of genus
$g\geq 2$
. We develop a new method for integrating over the representation space
$\mathbb {X}_{g,n}=\mathrm {Hom}(\Gamma _{g},S_{n})$
, where
$S_{n}$
is the symmetric group of permutations of
$\{1,\ldots ,n\}$
. Equivalently, this is the space of all vertex-labeled, n-sheeted covering spaces of the closed surface of genus g. |
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| ISSN: | 2050-5086 |