Formality in generalized Kähler geometry

Gil R. Cavalcanti

doi:10.1016/j.topol.2006.11.002

Formality in generalized Kähler geometry

Gil R. Cavalcanti^*

^*Corresponding author for this work

Mathematical Institute, St. Giles 24-29, Oxford, OX1 3LB, UK

Research output: Contribution to journal › Article › Academic › peer-review

Abstract

We prove that no nilpotent Lie algebra admits an invariant generalized Kähler structure. This is done by showing that a certain differential graded algebra associated to a generalized complex manifold is formal in the generalized Kähler case, while it is never formal for a generalized complex structure on a nilpotent Lie algebra.

Original language	English
Pages (from-to)	1119-1125
Number of pages	7
Journal	Topology and its Applications
Volume	154
Issue number	6
DOIs	https://doi.org/10.1016/j.topol.2006.11.002
Publication status	Published - 15 Mar 2007
Externally published	Yes

Keywords

Formality
Generalized Kähler
Nilmanifolds

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10.1016/j.topol.2006.11.002

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title = "Formality in generalized K{\"a}hler geometry",

abstract = "We prove that no nilpotent Lie algebra admits an invariant generalized K{\"a}hler structure. This is done by showing that a certain differential graded algebra associated to a generalized complex manifold is formal in the generalized K{\"a}hler case, while it is never formal for a generalized complex structure on a nilpotent Lie algebra.",

keywords = "Formality, Generalized K{\"a}hler, Nilmanifolds",

author = "Cavalcanti, {Gil R.}",

note = "Funding Information: I would like to thank Marco Gualtieri for his suggestions and inspired advice as well as Marisa Fern{\'a}ndez, Nigel Hitchin and Simon Salamon for suggestions on the first manuscript. I also thank IMPA for their hospitality while writing this paper. This research is supported by EPSRC.",

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PY - 2007/3/15

Y1 - 2007/3/15

N2 - We prove that no nilpotent Lie algebra admits an invariant generalized Kähler structure. This is done by showing that a certain differential graded algebra associated to a generalized complex manifold is formal in the generalized Kähler case, while it is never formal for a generalized complex structure on a nilpotent Lie algebra.

AB - We prove that no nilpotent Lie algebra admits an invariant generalized Kähler structure. This is done by showing that a certain differential graded algebra associated to a generalized complex manifold is formal in the generalized Kähler case, while it is never formal for a generalized complex structure on a nilpotent Lie algebra.

KW - Formality

KW - Generalized Kähler

KW - Nilmanifolds

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DO - 10.1016/j.topol.2006.11.002

M3 - Article

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SP - 1119

EP - 1125

JO - Topology and its Applications

JF - Topology and its Applications

IS - 6

ER -

Formality in generalized Kähler geometry

Abstract

Keywords

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