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On the Formality of Configuration Spaces of ℝn' × ℂn

  • Si Li
  • Peng Yang
  • Jiawei Zhou
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Abstract

This paper presents a complete classification of the formality of configuration spaces of ℝn' × ℂn. We define a constructible de Rham-Dolbeault cohomology theory which provides a constructible CDGA (commutative differential graded algebra) model of Confm(ℝn' × ℂn). For (n'=0,n≥2) or (n'=1,n≥1), the CDGAs are non-formal. For n'≥2,n≥1, we establish an explicit quasi-isomorphism between the constructible CDGA and its cohomology by using a diagrammatic CDGA of admissible diagrams and a regularized configuration space integral, which leads to the formality. As an application, we show that the local operator algebra of a topological-holomorphic field theory on ℝn' × ℂn (n'≥2,n≥1) is homotopically equivalent to a higher dimensional analog of vertex algebras.

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Cite

BibTeXRIS
BibTeX
@misc{li2026formality,
  title = {{On the Formality of Configuration Spaces of $\mathbbR^n' \times \mathbbC^n$}},
  author = {Si Li and Peng Yang and Jiawei Zhou},
  howpublished = {arXiv},
  year = {2026},
  month = aug,
  doi = {10.48550/arxiv.2608.28200},
  eprint = {2608.28200},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2608.28200},
}
RIS
TY  - UNPB
TI  - On the Formality of Configuration Spaces of ℝ^n' × ℂ^n
AU  - Si Li
AU  - Peng Yang
AU  - Jiawei Zhou
PY  - 2026
DA  - 2026/08/28
PB  - arXiv
DO  - 10.48550/arxiv.2608.28200
UR  - https://arxiv.org/abs/2608.28200
AB  - This paper presents a complete classification of the formality of configuration spaces of ℝ^n' × ℂ^n. We define a constructible de Rham-Dolbeault cohomology theory which provides a constructible CDGA (commutative differential graded algebra) model of Conf_m(ℝ^n' × ℂ^n). For (n'=0,n≥2) or (n'=1,n≥1), the CDGAs are non-formal. For n'≥2,n≥1, we establish an explicit quasi-isomorphism between the constructible CDGA and its cohomology by using a diagrammatic CDGA of admissible diagrams and a regularized configuration space integral, which leads to the formality. As an application, we show that the local operator algebra of a topological-holomorphic field theory on ℝ^n' × ℂ^n (n'≥2,n≥1) is homotopically equivalent to a higher dimensional analog of vertex algebras.
ER  -