Topological groupoids with involution and real algebraic stacks
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866916002043789312 |
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| author | Ambrosi, Emiliano Fortman, Olivier de Gaay |
| author_facet | Ambrosi, Emiliano Fortman, Olivier de Gaay |
| contents | To a topological groupoid endowed with an involution, we associate a topological groupoid of fixed points, generalizing the fixed-point subspace of a topological space with involution. We prove that when the topological groupoid with involution arises from a Deligne-Mumford stack over $\mathbb{R}$, this fixed locus coincides with the real locus of the stack. This provides a topological framework to study real algebraic stacks, and in particular real moduli spaces. Finally, we propose a Smith-Thom type conjecture in this setting, generalizing the Smith-Thom inequality for topological spaces endowed with an involution. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_02760 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Topological groupoids with involution and real algebraic stacks Ambrosi, Emiliano Fortman, Olivier de Gaay Algebraic Geometry Algebraic Topology General Topology To a topological groupoid endowed with an involution, we associate a topological groupoid of fixed points, generalizing the fixed-point subspace of a topological space with involution. We prove that when the topological groupoid with involution arises from a Deligne-Mumford stack over $\mathbb{R}$, this fixed locus coincides with the real locus of the stack. This provides a topological framework to study real algebraic stacks, and in particular real moduli spaces. Finally, we propose a Smith-Thom type conjecture in this setting, generalizing the Smith-Thom inequality for topological spaces endowed with an involution. |
| title | Topological groupoids with involution and real algebraic stacks |
| topic | Algebraic Geometry Algebraic Topology General Topology |
| url | https://arxiv.org/abs/2504.02760 |