A classical approach to smooth supermanifolds

Óscar Guajardo¹

¹ Unidad Cuernavaca del Instituto de Matemáticas UNAM Avenida Universidad s/n colonia Lomas de Chamilpa 62210, Cuernavaca, Morelos, México

Colloquium Mathematicum, Tome 148 (2017) no. 2, pp. 269-300

Résumé

A differential-geometric approach to supergeometry is considered, in the sense that our objects of study are superalgebra bundles over smooth manifolds. Our definition is not to be confused with Batchelor’s Theorem, for which we provide a direct proof. Rather, our objects are abstract superalgebra bundles, a special case of which are the so-called split supermanifolds constructed from the exterior algebra functor applied to a given vector bundle. The highlights of this work are the results proving equivalence between our approach and the usual “algebro-geometric” one using ringed spaces, and a supergeometric version of the Flowbox Theorem.

Détail

DOI : 10.4064/cm6772-7-2016

Keywords: differential geometric approach supergeometry considered sense objects study superalgebra bundles smooth manifolds definition confused batchelor theorem which provide direct proof rather objects abstract superalgebra bundles special which so called split supermanifolds constructed exterior algebra functor applied given vector bundle highlights work results proving equivalence between approach usual algebro geometric using ringed spaces supergeometric version flowbox theorem