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- Title
Monodromy Kernels for Strata of Translation Surfaces.
- Authors
Giannini, Riccardo
- 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 |$\mathcal {H}(3,1)$| and |$\mathcal {H}^{nh}(4)$| 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 |$\mathcal {H}(3,1)$| and |$\mathcal {H}^{nh}(4)$| are large, as they contain a non-abelian free group of rank |$2$|.
- Subjects
ORBIFOLDS; NONABELIAN groups; MONODROMY groups; FREE groups
- Publication
IMRN: International Mathematics Research Notices, 2024, Vol 2024, Issue 10, p8716
- ISSN
1073-7928
- Publication type
Article
- DOI
10.1093/imrn/rnae002