alpha-sloped Generalized Heegaard splittings of 3-manifolds

Marion Moore Campisi

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arXiv · 1102.3135

alpha-sloped Generalized Heegaard splittings of 3-manifolds

Marion Moore Campisi

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Abstract

We generalize the definition of thin position of Scharlemann and Thompson for compact orientable 3-manifolds with torus boundary components and introduce $\alpha$-sloped generalized Heegaard splittings. We examine its relationship to generalized Heegaard splittings of manifolds resulting from Dehn filling. We compare alpha-sloped thin position of 3-manifolds to other types of thin position for knots and 3-manifolds and discuss how this kind of decomposition gives an organic picture of M and allows the structure of the manifold to dictate the most natural slope(s) on the boundary. Additionally, we provide illustrative examples and questions motivating the study of alpha-sloped thin position.

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Marion Moore Campisi. 2011-02-15. alpha-sloped Generalized Heegaard splittings of 3-manifolds. https://arxiv.org/abs/1102.3135

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