Modular classes of Q-manifolds: a review and some applications

Andrew James Bruce

Archivum Mathematicum (2017)

  • Volume: 053, Issue: 4, page 203-219
  • ISSN: 0044-8753

Abstract

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A Q-manifold is a supermanifold equipped with an odd vector field that squares to zero. The notion of the modular class of a Q-manifold – which is viewed as the obstruction to the existence of a Q-invariant Berezin volume – is not well know. We review the basic ideas and then apply this technology to various examples, including L ∞ -algebroids and higher Poisson manifolds.

How to cite

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Bruce, Andrew James. "Modular classes of Q-manifolds: a review and some applications." Archivum Mathematicum 053.4 (2017): 203-219. <http://eudml.org/doc/294812>.

@article{Bruce2017,
abstract = {A Q-manifold is a supermanifold equipped with an odd vector field that squares to zero. The notion of the modular class of a Q-manifold – which is viewed as the obstruction to the existence of a Q-invariant Berezin volume – is not well know. We review the basic ideas and then apply this technology to various examples, including $L_\{\infty \}$-algebroids and higher Poisson manifolds.},
author = {Bruce, Andrew James},
journal = {Archivum Mathematicum},
keywords = {Q-manifolds; modular classes; characteristic classes; higher Poisson manifolds; $L_\{\infty \}$-algebroids},
language = {eng},
number = {4},
pages = {203-219},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {Modular classes of Q-manifolds: a review and some applications},
url = {http://eudml.org/doc/294812},
volume = {053},
year = {2017},
}

TY - JOUR
AU - Bruce, Andrew James
TI - Modular classes of Q-manifolds: a review and some applications
JO - Archivum Mathematicum
PY - 2017
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 053
IS - 4
SP - 203
EP - 219
AB - A Q-manifold is a supermanifold equipped with an odd vector field that squares to zero. The notion of the modular class of a Q-manifold – which is viewed as the obstruction to the existence of a Q-invariant Berezin volume – is not well know. We review the basic ideas and then apply this technology to various examples, including $L_{\infty }$-algebroids and higher Poisson manifolds.
LA - eng
KW - Q-manifolds; modular classes; characteristic classes; higher Poisson manifolds; $L_{\infty }$-algebroids
UR - http://eudml.org/doc/294812
ER -

References

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