Higher path groupoids and the holonomy of formal power series connections
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866913919514181632 |
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| author | Cellot, Matthew |
| author_facet | Cellot, Matthew |
| contents | Building on ideas of Kohno, we develop a framework for the construction of higher holonomy functors via the transport of formal power series connections. Using these techniques, we obtain functors from the path groupoid, the path 2-groupoid, and the path 3-groupoid of a manifold. As an application, we construct a Gray functor from the path 3-groupoid of the configuration space of $m$ points in $\mathbb{R}^n$ for $n\geqslant 4$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_23880 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Higher path groupoids and the holonomy of formal power series connections Cellot, Matthew Algebraic Topology Category Theory Quantum Algebra 53C29, 18N10, 18N20, 55U99 Building on ideas of Kohno, we develop a framework for the construction of higher holonomy functors via the transport of formal power series connections. Using these techniques, we obtain functors from the path groupoid, the path 2-groupoid, and the path 3-groupoid of a manifold. As an application, we construct a Gray functor from the path 3-groupoid of the configuration space of $m$ points in $\mathbb{R}^n$ for $n\geqslant 4$. |
| title | Higher path groupoids and the holonomy of formal power series connections |
| topic | Algebraic Topology Category Theory Quantum Algebra 53C29, 18N10, 18N20, 55U99 |
| url | https://arxiv.org/abs/2506.23880 |