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On the topology of $B\Gamma_n^\mathbb{C}$ and its application to complex structures on open manifolds https://arxiv.org/abs/2504.10610 #mathGT #mathCV

On the topology of $BΓ_n^\mathbb{C}$ and its application to complex structures on open manifolds

Since the 1970s, it has been known that any open connected manifold of dimension 2, 4 or 6 admits a complex analytic structure whenever its tangent bundle admits a complex linear structure. For half a century, this has been conjectured to hold true for manifolds of any dimension. In this paper, we extend the result to manifolds of dimension 8 and 10. The result is proved by applying Gromov's h-principle in order to adapt a method of Haefliger, originally used to study foliations, to the holomorphic setting. For dimension 12 and greater, the conjecture remains open.

arXiv.org
April 17, 2025 at 3:10 AM · · feed2toot · 0 · 0 · 0
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