353-combinatorial curvature and the $3$-dimensional $K(π,1)$ conjecture

Q: What type of study is this?

This is a Quantitative Study study.

Jingyin Huang; Piotr Przytycki

doi:10.48550/arxiv.2509.06914

September 8, 2025Open Access

353-combinatorial curvature and the $3$-dimensional $K(π,1)$ conjecture

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Key Points

The K(π,1) conjecture is validated for Artin groups in dimension 3, expanding its application.
A new form of combinatorial non-positive curvature is introduced as a foundational concept.
This work enhances the understanding of Artin groups and their dimensional properties.
The results may provoke further exploration into higher-dimensional applications of the conjecture.

Implication

We prove the K(π,1) conjecture for Artin groups in 3 dimensions, suggesting a new curvature form.

Abstract

We prove the $K(π,1)$ conjecture for Artin groups of dimension $3$. As an ingredient, we introduce a new form of combinatorial non-positive curvature.

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Cite This Study

Huang et al. (2025) studied this question.

synapsesocial.com/papers/68ec1be02b8fa9b2b78ad2ff https://doi.org/10.48550/arxiv.2509.06914

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353-combinatorial curvature and the $3$-dimensional $K(π,1)$ conjecture

Key Points

Implication

Abstract

Discussion

Cite This Study

353-combinatorial curvature and the $3$-dimensional $K(π,1)$ conjecture

Key Points

Implication

Abstract

Discussion

Cite This Study

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