Quillen equivalences for truncated multicomplexes

Jiahao Hu

arXiv:2608.07227v1 Primary: math.AT Secondary: math.DG

Abstract

We establish Quillen equivalences between successive truncations of multicomplexes for the model structures that detect weak equivalences simultaneously on prescribed pages of the two associated spectral sequences. In particular, the natural comparison from $4$-multicomplexes to bicomplexes, which is relevant to the comparison between almost complex and complex geometry, is a Quillen equivalence. This answers a question of Cirici, Livernet, and Whitehouse.

Disclosure

“Declaration on the use of artificial intelligence. OpenAI Codex (GPT-5 series, ac- cessed July–August 2026) was used as an interactive tool to explore proof strategies, check intermediate algebraic arguments, identify potentially relevant references, improve the or- ganization and language of the manuscript,”
PDF page 13

Classification: Proof ideas or individual proof-step assistance
Multiplier: 8
Verified: 2026-08-23T04:59:51.048511Z

Structural counts

Pages 14 pdf

Theorems 4 source

Lemmas 3 source

Propositions 4 source

Corollaries 4 source

Definitions 2 source

Displayed equations 61 source

Bibliography entries 20 source

Appendix pages 0 estimated

Count notes

Source counts use the expanded primary TeX file quillen_equivalence.tex.
Appendix pages include the first PDF page with an explicit Appendix heading through the final page.