Supermanifold Forms and Integration. A Dual Theory
| dc.creator | Voronov, Theodore | |
| dc.date | 1996-03-19 | |
| dc.date.accessioned | 2026-07-07T09:12:44Z | |
| dc.date.available | 2026-07-07T09:12:44Z | |
| dc.description | 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 $M^{n|m}\times\Bbb R^{r|s}$ 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 $\D:\Om{r}{s}\to\Om{r+1}{s}$ for $M^{n|m}$, where $0 \le s \le m$ and $r$ can be any integer. For $r\ge 0$ 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. | |
| dc.description | 20 pages, LaTeX2e, resubmitted after TeX changes | |
| dc.identifier | https://arxiv.org/abs/dg-ga/9603009 | |
| dc.identifier | http://arxiv.org/abs/dg-ga/9603009 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/152119 | |
| dc.subject | Differential Geometry | |
| dc.subject | High Energy Physics - Theory | |
| dc.subject | Quantum Algebra | |
| dc.title | Supermanifold Forms and Integration. A Dual Theory | |
| dc.type | text |