Header

UZH-Logo

Maintenance Infos

Moduli of coisotropic sections and the BFV-complex


Schätz, F (2011). Moduli of coisotropic sections and the BFV-complex. Asian Journal of Mathematics, 15(1):71-100.

Abstract

We consider the local deformation problem of coisotropic submanifolds inside symplectic
or Poisson manifolds. To this end the groupoid of coisotropic sections (with respect to some
tubular neighbourhood) is introduced. Although the geometric content of this groupoid is evident,
it is usually a very intricate object.
We provide a description of the groupoid of coisotropic sections in terms of a differential graded
Poisson algebra, called the BFV-complex. This description is achieved by constructing a groupoid
from the BFV-complex and a surjective morphism from this groupoid to the groupoid of coisotropic
sections. The kernel of this morphism can be easily chracterized.
As a corollary we obtain an isomorphism between the moduli space of coisotropic sections and
the moduli space of geometric Maurer–Cartan elements of the BFV-complex. In turn, this also sheds
new light on the geometric content of the BFV-complex.

Abstract

We consider the local deformation problem of coisotropic submanifolds inside symplectic
or Poisson manifolds. To this end the groupoid of coisotropic sections (with respect to some
tubular neighbourhood) is introduced. Although the geometric content of this groupoid is evident,
it is usually a very intricate object.
We provide a description of the groupoid of coisotropic sections in terms of a differential graded
Poisson algebra, called the BFV-complex. This description is achieved by constructing a groupoid
from the BFV-complex and a surjective morphism from this groupoid to the groupoid of coisotropic
sections. The kernel of this morphism can be easily chracterized.
As a corollary we obtain an isomorphism between the moduli space of coisotropic sections and
the moduli space of geometric Maurer–Cartan elements of the BFV-complex. In turn, this also sheds
new light on the geometric content of the BFV-complex.

Statistics

Citations

Dimensions.ai Metrics
2 citations in Web of Science®
2 citations in Scopus®
Google Scholar™

Altmetrics

Downloads

77 downloads since deposited on 18 May 2011
17 downloads since 12 months
Detailed statistics

Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Mathematics
Dewey Decimal Classification:510 Mathematics
Scopus Subject Areas:Physical Sciences > General Mathematics
Physical Sciences > Applied Mathematics
Language:English
Date:2011
Deposited On:18 May 2011 10:07
Last Modified:30 Jul 2020 01:17
Publisher:International Press
ISSN:1093-6106
OA Status:Hybrid
Publisher DOI:https://doi.org/10.4310/AJM.2011.v15.n1.a5
Related URLs:http://arxiv.org/pdf/0903.4074

Download

Hybrid Open Access

Download PDF  'Moduli of coisotropic sections and the BFV-complex'.
Preview
Content: Published Version
Filetype: PDF
Size: 1MB
View at publisher