Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2507.06246 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866911045780504576 |
|---|---|
| author | Yan, Zhiwei |
| author_facet | Yan, Zhiwei |
| contents | We present an intrinsic geometric classification of the supermanifold of maps from $\mathbb{R}^{0|2}$ to any smooth manifold $S$, avoiding auxiliary structures. The key isomorphism relates this space to the pullback of the decomposable bivector bundle over $S$, shown via algebraic constraints forcing odd vectors to be linearly dependent. The reduced manifold has fiber dimension $\dim S + 1$, unifying topological or algebraic views for a canonical framework in supersymmetric theories, distinct from prior works using connections. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_06246 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Intrinsic Parameterization of Supermanifold Morphisms from $\mathbb{R}^{0|2}$ via Decomposable Bivector Bundles Yan, Zhiwei Differential Geometry We present an intrinsic geometric classification of the supermanifold of maps from $\mathbb{R}^{0|2}$ to any smooth manifold $S$, avoiding auxiliary structures. The key isomorphism relates this space to the pullback of the decomposable bivector bundle over $S$, shown via algebraic constraints forcing odd vectors to be linearly dependent. The reduced manifold has fiber dimension $\dim S + 1$, unifying topological or algebraic views for a canonical framework in supersymmetric theories, distinct from prior works using connections. |
| title | Intrinsic Parameterization of Supermanifold Morphisms from $\mathbb{R}^{0|2}$ via Decomposable Bivector Bundles |
| topic | Differential Geometry |
| url | https://arxiv.org/abs/2507.06246 |