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Deformations of Pre-symplectic Structures and the Koszul L∞-algebra.
- Source :
-
IMRN: International Mathematics Research Notices . Jul2020, Vol. 2020 Issue 14, p4191-4237. 47p. - Publication Year :
- 2020
-
Abstract
- We study the deformation theory of pre-symplectic structures, that is, closed 2-forms of fixed rank. The main result is a parametrization of nearby deformations of a given pre-symplectic structure in terms of an |$L_{\infty }$| -algebra, which we call the Koszul |$L_{\infty }$| -algebra. This |$L_{\infty }$| -algebra is a cousin of the Koszul dg Lie algebra associated to a Poisson manifold. In addition, we show that a quotient of the Koszul |$L_{\infty }$| -algebra is isomorphic to the |$L_{\infty }$| -algebra that controls the deformations of the underlying characteristic foliation. Finally, we show that the infinitesimal deformations of pre-symplectic structures and of foliations are both obstructed. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 10737928
- Volume :
- 2020
- Issue :
- 14
- Database :
- Academic Search Index
- Journal :
- IMRN: International Mathematics Research Notices
- Publication Type :
- Academic Journal
- Accession number :
- 144757428
- Full Text :
- https://doi.org/10.1093/imrn/rny123