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Algèbre, géométrie, topologie
Holomorphic sl(2,C)–differential systems on compact Riemann surfaces and curves in compact quotients of SL(2,C)
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Europe/Paris
Description
We explain the framework, the motivations and the strategy behind a result that constructs holomorphic sl(2, C)–differential systems over some Riemann surfaces Σg of genus g ≥ 2, such that the image of the associated monodromy homomorphism lies in some cocompact Kleinian subgroup
Γ ⊂ SL(2, C). As a consequence, there exist holomorphic maps from Σg to the
quotient SL(2, C)/Γ, that do not factor through any elliptic curve. This answers positively a question asked by Huckleberry and Winkelmann, also raised by Ghys.
The talk is based on a joint work with Indranil Biswas (Shiv Nadar University, New Delhi), Lynn Heller (BIMSA, Beijing) and Sebastian Heller (BIMSA, Beijing).
