A necessary and sufficient condition for the existence of a supermanifold structure on a quotient defined by equivalence relation is proved. Furthermore, we show that an equivalence relation, R, on a supersmooth Berezin-Leites-Kostant supermanifold (graded manifold), X, determines a quotient supermanifold X/R if and only if the restriction, R_0, of R to the underlying smooth manifold, X_0, of X determines a quotient smooth manifold X_0/R_0.
Quotient supermanifolds
BARTOCCI, CLAUDIO;
1998-01-01
Abstract
A necessary and sufficient condition for the existence of a supermanifold structure on a quotient defined by equivalence relation is proved. Furthermore, we show that an equivalence relation, R, on a supersmooth Berezin-Leites-Kostant supermanifold (graded manifold), X, determines a quotient supermanifold X/R if and only if the restriction, R_0, of R to the underlying smooth manifold, X_0, of X determines a quotient smooth manifold X_0/R_0.
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