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Simultaneous deformations and poisson geometry


Frégier, Yaël; Zambon, Marco (2015). Simultaneous deformations and poisson geometry. Compositio Mathematica, 151(9):1763-1790.

Abstract

We consider the problem of deforming simultaneously a<jats:italic>pair</jats:italic>of given structures. We show that such deformations are governed by an<jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" mime-subtype="gif" xlink:href="S0010437X15007277_inline1" xlink:type="simple" /><jats:tex-math>$L_{\infty }$</jats:tex-math></jats:alternatives></jats:inline-formula>-algebra, which we construct explicitly. Our machinery is based on Voronov’s derived bracket construction. In this paper we consider only geometric applications, including deformations of coisotropic submanifolds in Poisson manifolds, of twisted Poisson structures, and of complex structures within generalized complex geometry. These applications cannot be, to our knowledge, obtained by other methods such as operad theory.

Abstract

We consider the problem of deforming simultaneously a<jats:italic>pair</jats:italic>of given structures. We show that such deformations are governed by an<jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" mime-subtype="gif" xlink:href="S0010437X15007277_inline1" xlink:type="simple" /><jats:tex-math>$L_{\infty }$</jats:tex-math></jats:alternatives></jats:inline-formula>-algebra, which we construct explicitly. Our machinery is based on Voronov’s derived bracket construction. In this paper we consider only geometric applications, including deformations of coisotropic submanifolds in Poisson manifolds, of twisted Poisson structures, and of complex structures within generalized complex geometry. These applications cannot be, to our knowledge, obtained by other methods such as operad theory.

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Item Type:Journal Article, refereed, original work
Communities & Collections:National licences > 142-005
Dewey Decimal Classification:Unspecified
Scopus Subject Areas:Physical Sciences > Algebra and Number Theory
Language:English
Date:1 September 2015
Deposited On:23 Oct 2018 16:37
Last Modified:01 Sep 2020 00:00
Publisher:Cambridge University Press
ISSN:0010-437X
OA Status:Green
Free access at:Publisher DOI. An embargo period may apply.
Publisher DOI:https://doi.org/10.1112/s0010437x15007277
Related URLs:https://www.swissbib.ch/Search/Results?lookfor=nationallicencecambridge101112S0010437X15007277 (Library Catalogue)

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