Abstract
We consider the SL(2,Z)-orbits of primitive n-squared origamis in the stratum H(2). In particular, we consider the 4-valent graphs obtained from the action of SL(2,Z) with respect to a generating set of size two. We prove that, apart from the orbit for n = 3 and one of the orbits for n = 5, all of the obtained graphs are non-planar. Specifically, in each of the graphs we exhibit a K3,3 minor, where K3,3 is the complete bipartite graph on two sets of three vertices.
| Original language | English |
|---|---|
| Pages (from-to) | 2258-2269 |
| Number of pages | 12 |
| Journal | Bulletin of the London Mathematical Society |
| Volume | 55 |
| Issue number | 5 |
| Early online date | 7 May 2023 |
| DOIs | |
| Publication status | E-pub ahead of print - 7 May 2023 |
Bibliographical note
Funding Information:The first author is thankful for support from the Heilbronn Institute for Mathematical Research. We thank Curtis McMullen for bringing additional references to our attention and for suggesting the investigation of the alternate generating set for . We also thank the anonymous referee for their careful reading of this article.
Publisher Copyright:
© 2022 The Authors. Bulletin of the London Mathematical Society is copyright © London Mathematical Society.