On spaces of embeddings of circles in surfaces
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arXiv
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866911383888592896 |
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| author | Gelnett, Ryan C. |
| author_facet | Gelnett, Ryan C. |
| contents | We consider the space of embeddings of finitely many circles that bound disks in non-positively curved surfaces. We index the connected components of this space with finite rooted trees and show that the connected components are classifying spaces of the ``braided" automorphism groups of the associated trees. An intermediate step to proving these results is to construct a strong deformation retract onto the subspace of geometric circles; moreover, this strong deformation retraction is equivariant with respect to transformations of the surface. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_12450 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | On spaces of embeddings of circles in surfaces Gelnett, Ryan C. Algebraic Topology Group Theory Geometric Topology 58D10 (Primary) 55R80, 20F65, 20F36 (Secondary) We consider the space of embeddings of finitely many circles that bound disks in non-positively curved surfaces. We index the connected components of this space with finite rooted trees and show that the connected components are classifying spaces of the ``braided" automorphism groups of the associated trees. An intermediate step to proving these results is to construct a strong deformation retract onto the subspace of geometric circles; moreover, this strong deformation retraction is equivariant with respect to transformations of the surface. |
| title | On spaces of embeddings of circles in surfaces |
| topic | Algebraic Topology Group Theory Geometric Topology 58D10 (Primary) 55R80, 20F65, 20F36 (Secondary) |
| url | https://arxiv.org/abs/2601.12450 |