A Decomposition Theorem for Topological Branched Coverings
Fuente:
arXiv
Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866908855719428096 |
|---|---|
| author | Sharaf, Shahryar Ghaed |
| author_facet | Sharaf, Shahryar Ghaed |
| contents | In the context of complex algebraic varieties, the decomposition theorem for semi-small maps provides a decomposition of the direct image of the constant sheaf. In this work, we develop a decomposition theorem for branched coverings of topological spaces. To achieve this, we start by constructing a decomposition theorem for unramified covering maps via an explicit gluing construction using transition functions. For a given branched covering of closed topological manifolds, we use the previous result to establish a decomposition of the direct image of the constant sheaf on the covering space. In the next step, we generalize our discussion to the case where the target space is not necessarily a topological manifold. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_05848 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A Decomposition Theorem for Topological Branched Coverings Sharaf, Shahryar Ghaed Algebraic Topology Algebraic Geometry In the context of complex algebraic varieties, the decomposition theorem for semi-small maps provides a decomposition of the direct image of the constant sheaf. In this work, we develop a decomposition theorem for branched coverings of topological spaces. To achieve this, we start by constructing a decomposition theorem for unramified covering maps via an explicit gluing construction using transition functions. For a given branched covering of closed topological manifolds, we use the previous result to establish a decomposition of the direct image of the constant sheaf on the covering space. In the next step, we generalize our discussion to the case where the target space is not necessarily a topological manifold. |
| title | A Decomposition Theorem for Topological Branched Coverings |
| topic | Algebraic Topology Algebraic Geometry |
| url | https://arxiv.org/abs/2512.05848 |