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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2409.04629 |
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Table of Contents:
- A harmonic cover of graphs $p:\widetilde{X}\to X$ induces a surjective pushforward morphism $p_*:\operatorname{Jac}(\widetilde{X})\to \operatorname{Jac}(X)$ on the critical groups. In the case when $p$ is Galois with abelian Galois group, we compute the order of the kernel of $p_*$, and hence the relationship between the numbers of spanning trees of $\widetilde{X}$ and $X$, in terms of Zaslavsky's bias matroid associated to the cover $p:\widetilde{X}\to X$.