Critical groups in harmonic abelian quotients
| Autor: | Vetluzhskikh, Mariia, Zakharov, Dmitry |
|---|---|
| Rok vydání: | 2024 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | 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 $p:\widetilde{X}\to X$. Comment: 30 pages, 5 figures |
| Databáze: | arXiv |
| Externí odkaz: |
|