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arXiv · 2302.08919

Pluripotential Homotopy Theory

Jonas Stelzig
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Abstract

We build free, bigraded bidifferential algebra models for the forms on a complex manifold, with respect to a strong notion of quasi-isomorphism and compatible with the conjugation symmetry. This answers a question of Sullivan. The resulting theory naturally accomodates higher operations involving double primitives. As applications, we obtain various refinements of the homotopy groups, sensitive to the complex structure. Under a simple connectedness assumption, one obtains minimal models which are unique up to isomorphism and allow for explicit computations of the new invariants.

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Jonas Stelzig. 2023-02-17. Pluripotential Homotopy Theory. https://doi.org/10.1016/j.aim.2024.110038

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