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首页> 外文期刊>Annales scientifiques de l'Ecole normale superieure >SO(n,n + 1)-SURFACE GROUP REPRESENTATIONS AND HIGGS BUNDLES
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SO(n,n + 1)-SURFACE GROUP REPRESENTATIONS AND HIGGS BUNDLES

机译：所以（n，n + 1）-surface组表示和hggs捆绑

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摘要

We study the character variety of representations of the fundamental group of a closed surface of genus g ≥ 2 into the Lie group SO(n,n + 1) using Higgs bundles. For each integer 0 < d ≤ n(2g - 2), we show there is a smooth connected component of the character variety which is diffeomorphic to the product of a certain vector bundle over a symmetric product of a Riemann surface with the vector space of holomorphic differentials of degree 2,4,..., 2n - 2. In particular, when d = n(2g - 2), this recovers Hitchin's parameterization of the Hitchin component. We also exhibit 22g+1 - 1 additional connected components of the SO (n, n + 1) -character variety and compute their topology. Moreover, representations in all of these new components cannot be continuously deformed to representations with compact Zariski closure. Using recent work of Guichard-Wienhard on positivity, it is shown that each of the representations which define singularities (i.e., those which are not irreducible) in these 22g+1 - 1 connected components are positive Anosov representations.
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