Abstract
The Heegaard genus of a 3-manifold, as well as the growth of Heegaard genus in its finite sheeted covering spaces, has extensively been studied in terms of alge-braic, geometric and topological properties of the 3-manifold. This note shows that analogous results concerning the trisection genus of a smooth, orientable 4-manifold have more general answers than their counterparts for 3-manifolds. In the case of hyperbolic 4-manifolds, upper and lower bounds are given in terms of volume and a trisection of the Davis manifold is described.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 395-402 |
| Number of pages | 8 |
| Journal | REVUE ROUMAINE DE MATHEMATIQUES PURES ET APPLIQUEES |
| Volume | 64 |
| Issue number | 4 |
| State | Published - 2019 |
| Externally published | Yes |
Bibliographical note
Funding Information:Acknowledgements. The authors thank David Gay, Jonathan Hillman and Jeff Meier for interesting and helpful comments. This work is supported by ARC Future Fellowship FT170100316.
Publisher Copyright:
© 2019 Editura Academiei Romane. All rights reserved.
Keywords
- Davis manifold
- Rank of group
- Stable trisection genus
- Triangulation complexity
- Trisection
- Trisection genus