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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2508.21057 |
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Table of 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.