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There is an isomorphism between the moduli spaces of $\sigma$-stableholomorphic triples and some of the critical submanifolds of the moduli spaceof $k$-Higgs bundles of rank three, whose elements $(E,\varphi^k)$ correspondto variations of Hodge structure, VHS. There are special embeddings on themoduli spaces of $k$-Higgs bundles of rank three. The main objective here is tostudy the cohomology of the critical submanifolds of such moduli spaces,extending those embeddings to moduli spaces of holomorphic triples.

Variations of Hodge Structures of Rank Three k-Higgs Bundles and Moduli Spaces of Holomorphic Triples