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| Format: | Preprint |
| Published: |
2025
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| Online Access: | https://arxiv.org/abs/2508.21057 |
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| _version_ | 1866909758343086080 |
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| author | Das, Sumanta |
| author_facet | Das, Sumanta |
| contents | A map between connected $2$-manifolds has a geometric kernel if it sends a non-contractible simple loop to a null-homotopic loop. While every non-$π_1$-injective map between compact surfaces admits a geometric kernel, this generally fails for compact bordered or non-compact surfaces. In this paper, we use Brown's proper fundamental group to give a sufficient condition under which a degree-one map between non-compact surfaces admits a geometric kernel. Furthermore, we characterize conjugacy classes in the proper fundamental group and use this characterization to establish sufficient conditions for the existence of geometric kernels. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_21057 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Geometric Kernels of Proper Maps Between Non-Compact Surfaces Das, Sumanta Geometric Topology Algebraic Topology 57K20 (Primary), 55S37 (Secondary) A map between connected $2$-manifolds has a geometric kernel if it sends a non-contractible simple loop to a null-homotopic loop. While every non-$π_1$-injective map between compact surfaces admits a geometric kernel, this generally fails for compact bordered or non-compact surfaces. In this paper, we use Brown's proper fundamental group to give a sufficient condition under which a degree-one map between non-compact surfaces admits a geometric kernel. Furthermore, we characterize conjugacy classes in the proper fundamental group and use this characterization to establish sufficient conditions for the existence of geometric kernels. |
| title | Geometric Kernels of Proper Maps Between Non-Compact Surfaces |
| topic | Geometric Topology Algebraic Topology 57K20 (Primary), 55S37 (Secondary) |
| url | https://arxiv.org/abs/2508.21057 |