Quillen superconnections and connections on supermanifolds

JOURNAL OF GEOMETRY AND PHYSICS

卷:86

Article

Beltran, Jose V.¹  Monterde, Juan¹  Vallejo, Jose A.² 

[1] Univ Valencia, Fac Matemat, Dept Geometria & Topol, E-46100 Burjassot, Valencia, Spain

[2] Univ Sonora, Dept Matemat, Hermosillo 83000, Sonora, Mexico

关键词: Superconnections;    Graded connections;    Supermanifolds;    Chern classes;   

DOI  :  10.1016/j.geomphys.2014.07.035

来源: Elsevier

【 摘 要 】

Given a supervector bundle E = E-0 circle plus E-1 -> M, we exhibit a parametrization of Quillen superconnections on E by graded connections on the Cartan-Moszul supermanifold (M, Omega(M)). The relation between the curvatures of both kind of connections, and their associated Chem 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. (C) 2014 Elsevier B.V. All rights reserved.

【 授权许可】

Free