On the real homotopy type of compact complex surfaces

Joana Cirici

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arXiv · 2601.01958

On the real homotopy type of compact complex surfaces

Joana Cirici

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Abstract

We show that on a compact complex surface all Massey products of cohomology classes in degree one vanish beyond length three. Dually, the real Malcev completion of the fundamental group is homogeneously presented by quadratic and cubic relations. In the non-K\"ahler case, we give an explicit presentation, which is determined by the first Betti number of the surface.

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Joana Cirici. 2026-01-05. On the real homotopy type of compact complex surfaces. https://arxiv.org/abs/2601.01958

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