No Access
Thurston norms of tunnel number-one manifolds
https://doi.org/10.1142/S0218216519500561Cited by:1 (Source: Crossref)
Abstract
The Thurston norm of a three-manifold measures the complexity of surfaces representing two-dimensional homology classes. We study the possible unit balls of Thurston norms of three-manifolds with , and whose fundamental groups admit presentations with two generators and one relator. We show that even among this special class, there are three-manifolds such that the unit ball of the Thurston norm has arbitrarily many faces.
AMSC: 57M27, 57M05, 20J05, 20J06, 57R19
References
- 1. , Convergence groups and Seifert fibered 3-manifolds, Invent. Math. 118(3) (1994) 441–456. Crossref, Web of Science, Google Scholar
- 2. , A random tunnel number one 3-manifold does not fiber over the circle, Geom. Topol. 10 (2006) 2431–2499. Crossref, Web of Science, Google Scholar
- 3. , Primer on Mapping Class Groups (Princeton University Press, 2012). Google Scholar
- 4. S. Friedl and S. Tillman, Two-Generator One-Relator Groups and Marked Polytopes, accepted, Annales de l’Institut Fourier. arXiv:1501.03489. Google Scholar
- 5. , Thurston Norm and Fox Calculus, Geom. Topol. 21 (2017) 3759–3784. Crossref, Web of Science, Google Scholar
- 6. , Convergence groups are Fuchsian groups, Ann. Math. 136(3) (1992) 447–510. Crossref, Web of Science, Google Scholar
- 7. , The Thurston polytope for four-stranded pretzel links, Alg. Geom. Topol. 8 (2008) 211–243. Crossref, Web of Science, Google Scholar
- 8. , There are no fake Seifert fibre spaces with infinite , Ann. Math. 170 (1983) 35–70. Crossref, Web of Science, Google Scholar
- 9. , A norm for the homology of 3–manifolds, Mem. Amer. Math. Soc. 59 (1986) 99–130. Web of Science, Google Scholar
