Bott-Chern and Aeppli homotopy

Jiahao Hu

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arXiv · 2606.13224

Bott-Chern and Aeppli homotopy

Jiahao Hu

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Abstract

This paper introduces Bott-Chern and Aeppli homotopy sets for a fibrant class of bisimplicial sets and establishes their basic properties. In positive bidegrees, Bott-Chern homotopy sets carry natural monoid structures, while Aeppli homotopy sets carry natural group structures. They are related by a loop-space comparison: after a bidegree shift, the Aeppli homotopy groups of X are naturally identified with the Bott-Chern homotopy monoids of the loop space of X. In particular, the Bott-Chern homotopy monoids of loop spaces are groups. To justify our definitions, we show that the Bott-Chern homotopy monoids of a bisimplicial abelian group are naturally isomorphic to the Bott-Chern homology groups of its associated normalized Moore bicomplex. An analogous statement holds for Aeppli homotopy.

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BibTeX RIS

Jiahao Hu. 2026-06-11. Bott-Chern and Aeppli homotopy. https://arxiv.org/abs/2606.13224

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