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|Type:||Artigo de periódico|
|Title:||Complex Hyperbolic Structures on Disc Bundles over Surfaces|
|Abstract:||We study complex hyperbolic disc bundles over closed orientable surfaces that arise from discrete and faithful representations H(n) -> PU(2, 1), where H(n) is the fundamental group of the orbifold S(2)(2, ... ,2) and thus contains a surface group as a subgroup of index 2 or 4. The results obtained provide the first complex hyperbolic disc bundles M -> Sigma that admit both real and complex hyperbolic structures, satisfy the equality 2(chi + e) = 3 tau, satisfy the inequality 1/2 chi < e, and induce discrete and faithful representations pi(1)Sigma -> PU( 2, 1) with fractional Toledo invariant, where chi is the Euler characteristic of Sigma, e denotes the Euler number of M, and tau stands for the Toledo invariant of M. To obtain a satisfactory explanation of the equality 2(chi + e) = 3 tau, we conjecture that there exists a holomorphic section in all our examples. In order to reduce the amount of calculations, we systematically explore coordinate-free methods.|
|Editor:||Oxford Univ Press|
|Appears in Collections:||Unicamp - Artigos e Outros Documentos|
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