Abstract
Graph coverings are known to induce surjections of their critical groups. Here we describe the kernels of these morphisms in terms of data parametrizing the covering. Regular coverings are parametrized by voltage graphs, and the above kernel can be identified with a naturally defined voltage graph critical group. For double covers, the voltage graph is a signed graph, and the theory takes a particularly pleasant form, leading also to a theory of double covers of signed graphs.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 10-40 |
| Number of pages | 31 |
| Journal | Discrete Mathematics |
| Volume | 318 |
| Issue number | 1 |
| DOIs | |
| State | Published - Mar 6 2014 |
Bibliographical note
Funding Information:This project was undertaken during an REU at the University of Minnesota School of Mathematics in Summer 2012, co-mentored by G. Musiker, P. Pylyavskyy, V. Reiner and D. Stanton, and supported by NSF RTG grant number DMS-1148634 . The authors thank the participants during this REU for their helpful comments and suggestions throughout.
Keywords
- Covering
- Critical
- Crown
- Double
- Functorial
- Graph
- Morphism
- Sandpile group
- Signed
- Voltage