Quillen superconnections and connections on supermanifolds

J. V. Beltrán; J. Monterde; J. A. Vallejo

doi:10.1016/j.geomphys.2014.07.035

Quillen superconnections and connections on supermanifolds

Differential Geometry 2015-06-15 v1 High Energy Physics - Theory Mathematical Physics math.MP

Authors: J. V. Beltrán , J. Monterde , J. A. Vallejo

View on arXiv ↗ PDF ↗ DOI ↗

Abstract

Given a supervector bundle $E = E_0\oplus E_1 \to M$ , we exhibit a parametrization of Quillen superconnections on $E$ by graded connections on the Cartan-Koszul supermanifold $(M;\Omega (M))$ . The relation between the curvatures of both kind of connections, and their associated Chern classes, is discussed in detail. In particular, we find that Chern classes for graded vector bundles on split supermanifolds can be computed through the associated Quillen superconnections.

Keywords

Quillen superconnections supermanifolds graded connections Cartan-Koszul supermanifold curvature Chern classes supervector bundles

Cite

@article{arxiv.1305.3677,
  title  = {Quillen superconnections and connections on supermanifolds},
  author = {J. V. Beltrán and J. Monterde and J. A. Vallejo},
  journal= {arXiv preprint arXiv:1305.3677},
  year   = {2015}
}

Comments

First version

Quillen superconnections and connections on supermanifolds

Abstract

Keywords

Cite

Comments

Related papers