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Curved infinity-algebras and their characteristic classes

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Curved infinity-algebras and their characteristic classes. / Lazarev, Andrey; Schedler, Travis.
In: Journal of Topology, Vol. 5, No. 3, 2012, p. 503-528.

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

Harvard

Lazarev, A & Schedler, T 2012, 'Curved infinity-algebras and their characteristic classes', Journal of Topology, vol. 5, no. 3, pp. 503-528. https://doi.org/10.1112/jtopol/jts011

APA

Lazarev, A., & Schedler, T. (2012). Curved infinity-algebras and their characteristic classes. Journal of Topology, 5(3), 503-528. https://doi.org/10.1112/jtopol/jts011

Vancouver

Lazarev A, Schedler T. Curved infinity-algebras and their characteristic classes. Journal of Topology. 2012;5(3):503-528. doi: 10.1112/jtopol/jts011

Author

Lazarev, Andrey ; Schedler, Travis. / Curved infinity-algebras and their characteristic classes. In: Journal of Topology. 2012 ; Vol. 5, No. 3. pp. 503-528.

Bibtex

@article{413315fd290b4d0d8cb56c2478ebd305,
title = "Curved infinity-algebras and their characteristic classes",
abstract = "In this paper, we study a natural extension of Kontsevich's characteristic class construction for A∞- and L∞-algebras to the case of curved algebras. These define homology classes on a variant of his graph homology that allows vertices of valence at least 1. We compute this graph homology, which is governed by star-shaped graphs with odd-valence vertices. We also classify non-trivially curved cyclic A∞- and L∞- algebras over a field up to gauge equivalence, and show that these are essentially reduced to algebras of dimension at most 2 with only even-ary operations. We apply the reasoning to compute stability maps for the homology of Lie algebras of formal vector fields. Finally, we explain a generalization of these results to other types of algebras, using the language of operads. A key observation is that operads governing curved algebras are closely related to the Koszul dual of those governing unital algebras.",
author = "Andrey Lazarev and Travis Schedler",
year = "2012",
doi = "10.1112/jtopol/jts011",
language = "English",
volume = "5",
pages = "503--528",
journal = "Journal of Topology",
issn = "1753-8416",
publisher = "John Wiley and Sons Ltd",
number = "3",

}

RIS

TY - JOUR

T1 - Curved infinity-algebras and their characteristic classes

AU - Lazarev, Andrey

AU - Schedler, Travis

PY - 2012

Y1 - 2012

N2 - In this paper, we study a natural extension of Kontsevich's characteristic class construction for A∞- and L∞-algebras to the case of curved algebras. These define homology classes on a variant of his graph homology that allows vertices of valence at least 1. We compute this graph homology, which is governed by star-shaped graphs with odd-valence vertices. We also classify non-trivially curved cyclic A∞- and L∞- algebras over a field up to gauge equivalence, and show that these are essentially reduced to algebras of dimension at most 2 with only even-ary operations. We apply the reasoning to compute stability maps for the homology of Lie algebras of formal vector fields. Finally, we explain a generalization of these results to other types of algebras, using the language of operads. A key observation is that operads governing curved algebras are closely related to the Koszul dual of those governing unital algebras.

AB - In this paper, we study a natural extension of Kontsevich's characteristic class construction for A∞- and L∞-algebras to the case of curved algebras. These define homology classes on a variant of his graph homology that allows vertices of valence at least 1. We compute this graph homology, which is governed by star-shaped graphs with odd-valence vertices. We also classify non-trivially curved cyclic A∞- and L∞- algebras over a field up to gauge equivalence, and show that these are essentially reduced to algebras of dimension at most 2 with only even-ary operations. We apply the reasoning to compute stability maps for the homology of Lie algebras of formal vector fields. Finally, we explain a generalization of these results to other types of algebras, using the language of operads. A key observation is that operads governing curved algebras are closely related to the Koszul dual of those governing unital algebras.

U2 - 10.1112/jtopol/jts011

DO - 10.1112/jtopol/jts011

M3 - Journal article

VL - 5

SP - 503

EP - 528

JO - Journal of Topology

JF - Journal of Topology

SN - 1753-8416

IS - 3

ER -