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Maurer-Cartan moduli and theorems of Riemann-Hilbert type

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Maurer-Cartan moduli and theorems of Riemann-Hilbert type. / Chuang, Joseph; Holstein, Julian; Lazarev, Andrey.
In: Applied Categorical Structures, Vol. 29, No. 4, 31.08.2021, p. 685-728.

Research output: Contribution to Journal/Magazine › Journal article › peer-review

Harvard

Chuang, J, Holstein, J & Lazarev, A 2021, 'Maurer-Cartan moduli and theorems of Riemann-Hilbert type', Applied Categorical Structures, vol. 29, no. 4, pp. 685-728. https://doi.org/10.1007/s10485-021-09631-3

APA

Chuang, J., Holstein, J., & Lazarev, A. (2021). Maurer-Cartan moduli and theorems of Riemann-Hilbert type. Applied Categorical Structures, 29(4), 685-728. https://doi.org/10.1007/s10485-021-09631-3

Vancouver

Chuang J, Holstein J, Lazarev A. Maurer-Cartan moduli and theorems of Riemann-Hilbert type. Applied Categorical Structures. 2021 Aug 31;29(4):685-728. Epub 2021 Feb 6. doi: 10.1007/s10485-021-09631-3

Author

Chuang, Joseph ; Holstein, Julian ; Lazarev, Andrey. / Maurer-Cartan moduli and theorems of Riemann-Hilbert type. In: Applied Categorical Structures. 2021 ; Vol. 29, No. 4. pp. 685-728.

Bibtex

@article{79300700073944ccad25db6e7b21865b,
title = "Maurer-Cartan moduli and theorems of Riemann-Hilbert type",
abstract = "We study Maurer–Cartan moduli spaces of dg algebras and associated dg categories and show that, while not quasi-isomorphism invariants, they are invariants of strong homotopy type, a natural notion that has not been studied before. We prove, in several different contexts, Schlessinger–Stasheff type theorems comparing the notions of homotopy and gauge equivalence for Maurer–Cartan elements as well as their categorified versions. As an application, we re-prove and generalize Block–Smith{\textquoteright}s higher Riemann–Hilbert correspondence, and develop its analogue for simplicial complexes and topological spaces.",
keywords = "Maurer-Cartan element, Differential graded algebra, Simplicial complex, Smooth manifold, Locally constant sheaf",
author = "Joseph Chuang and Julian Holstein and Andrey Lazarev",
year = "2021",
month = aug,
day = "31",
doi = "10.1007/s10485-021-09631-3",
language = "English",
volume = "29",
pages = "685--728",
journal = "Applied Categorical Structures",
issn = "1572-9095",
publisher = "Springer",
number = "4",

}

RIS

TY - JOUR

T1 - Maurer-Cartan moduli and theorems of Riemann-Hilbert type

AU - Chuang, Joseph

AU - Holstein, Julian

AU - Lazarev, Andrey

PY - 2021/8/31

Y1 - 2021/8/31

N2 - We study Maurer–Cartan moduli spaces of dg algebras and associated dg categories and show that, while not quasi-isomorphism invariants, they are invariants of strong homotopy type, a natural notion that has not been studied before. We prove, in several different contexts, Schlessinger–Stasheff type theorems comparing the notions of homotopy and gauge equivalence for Maurer–Cartan elements as well as their categorified versions. As an application, we re-prove and generalize Block–Smith’s higher Riemann–Hilbert correspondence, and develop its analogue for simplicial complexes and topological spaces.

AB - We study Maurer–Cartan moduli spaces of dg algebras and associated dg categories and show that, while not quasi-isomorphism invariants, they are invariants of strong homotopy type, a natural notion that has not been studied before. We prove, in several different contexts, Schlessinger–Stasheff type theorems comparing the notions of homotopy and gauge equivalence for Maurer–Cartan elements as well as their categorified versions. As an application, we re-prove and generalize Block–Smith’s higher Riemann–Hilbert correspondence, and develop its analogue for simplicial complexes and topological spaces.

KW - Maurer-Cartan element

KW - Differential graded algebra

KW - Simplicial complex

KW - Smooth manifold

KW - Locally constant sheaf

U2 - 10.1007/s10485-021-09631-3

DO - 10.1007/s10485-021-09631-3

M3 - Journal article

VL - 29

SP - 685

EP - 728

JO - Applied Categorical Structures

JF - Applied Categorical Structures

SN - 1572-9095

IS - 4

ER -