The DOI matches its Crossref record; 8 of the 8 references it cites were found in a registry or an index.
Lie theory for nilpotent L∞-algebras
Open accessAbstract
The Deligne groupoid is a functor from nilpotent differential graded Lie algebras concentrated in positive degrees to groupoids; in the special case of Lie algebras over a field of characteristic zero, it gives the associated simply connected Lie group.We generalize the Deligne groupoid to a functor from L 1 -algebras concentrated in degree > n to n-groupoids.(We actually construct the nerve of the n-groupoid, which is an enriched Kan complex.)The construction of gamma is quite explicit (it is based on Dupont's proof of the de Rham theorem) and yields higher dimensional analogues of holonomy and of the Campbell-Hausdorff formula.In the case of abelian L 1 algebras (i.e., chain complexes), the functor is the Dold-Kan simplicial set.
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Cites
Infinitesimal computations in topology
Sullivan, D. (1977) · Publications mathématiques de l IHÉS · doi:10.1007/bf02684341 · Cited by 1,421 · cited 9×
“There is a close relationship between the Maurer-Cartan set and Sullivan’s functor Spec•(A), which we now explain.”
BackgroundMethodInfluentialWhitney, H. (1957) · doi:10.1515/9781400877577 · Cited by 1,391
Quillen, D. (1969) · The Annals of Mathematics · doi:10.2307/1970725 · Cited by 1,243
The deformation theory of representations of fundamental groups of compact Kähler manifolds
Goldman, W. M., & Millson, J. J. (1988) · Publications mathématiques de l IHÉS · doi:10.1007/bf02699127 · Cited by 353
Homology of Symmetric Products and Other Functors of Complexes
Dold, A. (1958) · Annals of Mathematics · doi:10.2307/1970043 · Cited by 274
Simplicial de rham cohomology and characteristic classes of flat bundles
Dupont, J. L. (1976) · Topology · doi:10.1016/0040-9383(76)90038-0 · Cited by 188
On the Locally Complete Families of Complex Analytic Structures
Kuranishi, M. (1962) · The Annals of Mathematics · doi:10.2307/1970211 · Cited by 161
Applications of perturbation theory to iterated fibrations
Lambe, L. A., & Stasheff, J. (1987) · manuscripta mathematica · doi:10.1007/bf01165893 · Cited by 99
Metadata
- Authors
- Getzler, E.
- Venue
- Annals of Mathematics
- Publisher
- Annals of Mathematics
- Published
- 2009-07-12
- Volume
- 170
- Issue
- 1
- Pages
- 271-301
- ISSN
- 0003-486X (ISSN-L)
- OpenAlex
- W2952549800
- Cited by
- 282
- References
- 8
- FWCI
- 20.35
- Type
- journal article
- Language
- en
- Open access
- bronze
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