Thurston norms of tunnel number-one manifolds

Natalia Pacheco-Tallaj; Kevin Schreve; Nicholas G. Vlamis

doi:10.1142/s0218216519500561

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arXiv · 1803.05097

Thurston norms of tunnel number-one manifolds

Natalia Pacheco-Tallaj·Kevin Schreve·Nicholas G. Vlamis

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Abstract

The Thurston norm of a 3-manifold measures the complexity of surfaces representing two-dimensional homology classes. We study the possible unit balls of Thurston norms of 3-manifolds $M$ with $b_1(M) = 2$, and whose fundamental groups admit presentations with two generators and one relator. We show that even among this special class, there are 3-manifolds such that the unit ball of the Thurston norm has arbitrarily many faces.

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BibTeX RIS

Natalia Pacheco-Tallaj, Kevin Schreve, Nicholas G. Vlamis. 2018-03-14. Thurston norms of tunnel number-one manifolds. https://doi.org/10.1142/s0218216519500561

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