# Construction of Maurer-Cartan elements over configuration spaces of curves

Abstract : For C a complex curve and n ≥ 1, a pair ($P$, $\Delta_P$) of a principal bundle $P$ with meromorphic flat connection over $C^n$ , holomorphic over the configuration space $C_n(C)$ of n points over $C$, was introduced in [En]. For any point ∞ ∈ C, we construct a trivialisation of the restriction of P to (C \ ∞)$^n$ and obtain a Maurer-Cartan element $J$ over $C_n$(C \ ∞) out of $\Delta_P$ , thus generalising a construction of Levin and Racinet when the genus of C is higher than one. We give explicit formulas for J as well as for $\Delta_P$. When n = 1, this construction gives rise to elements of Hain's space of second kind iterated integrals over C.
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Preprints, Working Papers, ...

https://hal-cea.archives-ouvertes.fr/cea-03406087
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Submitted on : Wednesday, October 27, 2021 - 4:17:35 PM
Last modification on : Saturday, October 30, 2021 - 3:50:59 AM

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### Identifiers

• HAL Id : cea-03406087, version 1
• ARXIV : 2110.09341

### Citation

Benjamin Enriquez, Federico Zerbini. Construction of Maurer-Cartan elements over configuration spaces of curves. 2021. ⟨cea-03406087⟩

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