1996/03/19 by Theodore Voronov, Voronov, Theodore · 1 citation
Mathematics · Physics and Astronomy · #Differential Geometry (math.DG) #FOS: Mathematics #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Quantum Algebra (math.QA) #dg-ga #hep-th #math.DG #math.QA #q-alg
paper · pdf · doi:10.48550/arxiv.dg-ga/9603009
20 pages, LaTeX2e, resubmitted after TeX changes
arxiv created 1996/03/19 · arxiv updated 2009/11/30
We investigate forms on supermanifolds defined as Lagrangians of ``copaths'' (that is, systems of equations, which may or may not specify submanifolds). For this, we consider direct products Mn|m×\Bbb Rr|s and study isomorphisms corresponding to simultaneously advancing the number of additional parameters r|s and the number of equations. We define an exteriour differential in terms of variational derivatives w.r.t. a copath and establish its main properties. In the resulting stable picture we obtain infinite complexes \D:\Omrs→\Omr+1s for Mn|m, where 0 ≤ s ≤ m and r can be any integer. For r≥ 0 a canonical isomorphism with forms constructed as Lagrangians of r|s-paths is established. We discover the ``lacking half'' of forms on supermanifolds: r|s-forms with r<0, previously unknown except for s=m. (They have been partly replaced earlier by an augmentation of the ``non-negative'' part of the complexes.) All these results are new. The study of these questions is in progress now.