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arXiv · 1906.05859

FAQ on the g-theorem and the hard Lefschetz theorem for face rings

Karim Adiprasito
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Abstract

This short review is the result of a minicourse at the Sapienza University of Rome the author gave about the proof of the $g$-theorem. We review the hard Lefschetz theorem for simplicial spheres, as well as the theory at its core: perturbations of maps, biased Poincaré pairings and a cobordism argument that relates the Lefschetz property of a manifold to the Lefschetz property on its boundary. We also sketch an alternative argument based on edge-contractions.

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Karim Adiprasito. 2019-08-22. FAQ on the g-theorem and the hard Lefschetz theorem for face rings. https://arxiv.org/abs/1906.05859

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