Foundations of geometric cohomology: from co-orientations to product structures
Fuente:
arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2022
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| Subjects: | |
| Online Access: | |
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| _version_ | 1866914518409412608 |
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| author | Friedman, Greg Medina-Mardones, Anibal M. Sinha, Dev |
| author_facet | Friedman, Greg Medina-Mardones, Anibal M. Sinha, Dev |
| contents | This manuscript develops a geometric approach to ordinary cohomology of smooth manifolds, constructing a cochain complex model based on co-oriented smooth maps from manifolds with corners. Special attention is given to the pull-back product of such smooth maps, which provides our geometric cochains with a partially defined product structure inducing the cup product in cohomology. A parallel treatment of homology is also given allowing for a geometric unification of the contravariant and covariant theories. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2212_07482 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Foundations of geometric cohomology: from co-orientations to product structures Friedman, Greg Medina-Mardones, Anibal M. Sinha, Dev Algebraic Topology Geometric Topology This manuscript develops a geometric approach to ordinary cohomology of smooth manifolds, constructing a cochain complex model based on co-oriented smooth maps from manifolds with corners. Special attention is given to the pull-back product of such smooth maps, which provides our geometric cochains with a partially defined product structure inducing the cup product in cohomology. A parallel treatment of homology is also given allowing for a geometric unification of the contravariant and covariant theories. |
| title | Foundations of geometric cohomology: from co-orientations to product structures |
| topic | Algebraic Topology Geometric Topology |
| url | https://arxiv.org/abs/2212.07482 |