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An $\mathsf A_\infty$
version of the Poincaré lemma
Camilo Arias Abad, Alexander Quintero Vélez and Sebastián Vélez Vásquez |
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Vol. 302 (2019), No. 2, 385–412
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Abstract |
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We prove a categorified version of the Poincaré lemma. The natural setting for our result is that of -local systems. More precisely, we show that any smooth homotopy between maps and induces an -natural transformation between the corresponding pullback functors. This transformation is explicitly defined in terms of Chen’s iterated integrals. In particular, we show that a homotopy equivalence induces a quasiequivalence on the DG categories of -local system. |
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Keywords
$\infty$-local system, DG category, DG functor, $\mathsf
A_\infty$-natural transformation, iterated integral
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Mathematical Subject Classification 2010
Primary: 55P65
Secondary: 51H25
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Milestones
Received: 29 August 2018
Revised: 25 January 2019
Accepted: 16 March 2019
Published: 27 November 2019
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Authors |
| Camilo Arias Abad | |
| Escuela de matemáticas Universidad Nacional de Colombia Sede Medellín Medellín Colombia |
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| Alexander Quintero Vélez | |
| Escuela de matemáticas Universidad Nacional de Colombia Sede Medellín Medellín Colombia |
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| Sebastián Vélez Vásquez | |
| Escuela de matemáticas Universidad Nacional de Colombia Sede Medellín Medellín Colombia |
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