Higher holonomy for curved L${}_\infty$-algebras 1: simplicial methods
| Autor: | Getzler, Ezra |
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| Rok vydání: | 2024 |
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| Druh dokumentu: | Working Paper |
| Popis: | We construct a natural morphism $\rho$ from the nerve $\text{MC}_\bullet(L) = \text{MC}(\Omega_\bullet \widehat{\otimes} L)$ of a pronilpotent curved L${}_\infty$-algebra $L$ to the simplicial subset $\gamma_\bullet(L) = \text{MC}(\Omega_\bullet \widehat{\otimes} L,s_\bullet)$ of Maurer--Cartan element satisfying the Dupont gauge condition. This morphism equals the identity on the image of the inclusion $\gamma_\bullet(L) \hookrightarrow \text{MC}_\bullet(L)$. The proof uses the extension of Berglund's homotopical perturbation theory for L${}_\infty$-algebras to curved L${}_\infty$-algebras. The morphism $\rho$ equals the holonomy for nilpotent Lie algebras. In a sequel to this paper, we use a cubical analogue $\rho^\square$ of $\rho$ to identify $\rho$ with higher holonomy for semiabelian curved \Linf-algebras. Comment: 17 pages |
| Databáze: | arXiv |
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