Geometric structures for the G2′ -Hitchin component
Advances in Mathematics, ISSN: 0001-8708, Vol: 462, Page: 110091
2025
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Article Description
We give an explicit geometric structures interpretation of the G2′ -Hitchin component Hit(S,G2′)⊂χ(π1S,G2′) of a closed oriented surface S of genus g≥2. In particular, we prove Hit(S,G2′) is naturally homeomorphic to a moduli space M of (G,X) -structures for G=G2′ and X=Ein2,3 on a fiber bundle C over S via the descended holonomy map. Explicitly, C is the direct sum of fiber bundles Image 1 with fiber Cp=UTpS×UTpS×R+, where UTS denotes the unit tangent bundle. The geometric structure associated to a G2′ -Hitchin representation ρ is explicitly constructed from the unique associated ρ -equivariant alternating almost-complex curve νˆ:S˜→Sˆ2,4 ; we critically use recent work of Collier-Toulisse on the moduli space of such curves. Our explicit geometric structures are examined in the G2′ -Fuchsian case and shown to be unrelated to the (G2′,Ein2,3) -structures of Guichard-Wienhard.
Bibliographic Details
http://www.sciencedirect.com/science/article/pii/S0001870824006078; http://dx.doi.org/10.1016/j.aim.2024.110091; http://www.scopus.com/inward/record.url?partnerID=HzOxMe3b&scp=85213494809&origin=inward; https://linkinghub.elsevier.com/retrieve/pii/S0001870824006078; https://dx.doi.org/10.1016/j.aim.2024.110091
Elsevier BV
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