Spun normal surfaces in 3-manifolds III: Boundary slopes

Kang, E.; Rubinstein, J.

doi:10.1090/proc/16031

Spun normal surfaces in 3-manifolds III: Boundary slopes
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by E. Kang and J. H. Rubinstein

Proc. Amer. Math. Soc. 150 (2022), 4053-4066

DOI: https://doi.org/10.1090/proc/16031

Published electronically: June 3, 2022

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Abstract:

Spun normal surfaces are a useful way of representing proper essential surfaces, using ideal triangulations for 3-manifolds with tori and Klein bottle boundaries. In this paper, we consider spinning essential surfaces in an irreducible $P^2$-irreducible, anannular, atoroidal 3-manifold with tori and Klein bottle boundary components. We can assume that such a 3-manifold is equipped with an ideal 1-efficient triangulation. In particular, we prove that for a given choice of a set of boundary slopes for a proper essential surface, there is a set of essential vertex solutions for the projective solution space at these boundary slopes, answering a question of Dunfield and Garoufalidis [Trans. Amer. Math. Soc. 364 (2012), pp. 6109–6137], so long as the slopes are not of a fiber of a bundle structure.

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