Giannini, R. (2024) Monodromy kernels for strata of translation surfaces. International Mathematics Research Notices, (doi: 10.1093/imrn/rnae002) (Early Online Publication)
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Abstract
The non-hyperelliptic connected components of the strata of translation surfaces are conjectured to be orbifold classifying spaces for some groups commensurable to some mapping class groups. The topological monodromy map of the non-hyperelliptic components projects naturally to the mapping class group of the underlying punctured surface and is an obvious candidate to test commensurability. In the present article, we prove that for the components H(3, 1) and Hnh(4) in genus 3 the monodromy map fails to demonstrate the conjectured commensurability. In particular, building on the work of Wajnryb, we prove that the kernels of the monodromy maps for H(3, 1) and Hnh(4) are large, as they contain a non-abelian free group of rank 2.
| Item Type: | Articles |
|---|---|
| Additional Information: | The author was supported by EPSRC grant EP/T517896/1. |
| Status: | Early Online Publication |
| Refereed: | Yes |
| Glasgow Author(s) Enlighten ID: | Giannini, Riccardo |
| Authors: | Giannini, R. |
| College/School: | College of Science and Engineering |
| Journal Name: | International Mathematics Research Notices |
| Publisher: | Oxford University Press |
| ISSN: | 1073-7928 |
| ISSN (Online): | 1687-0247 |
| Published Online: | 24 January 2024 |
| Copyright Holders: | Copyright © The Author(s) 2024 |
| First Published: | First published in International Mathematics Research Notices 2024 |
| Publisher Policy: | Reproduced under a Creative Commons licence |
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