arXiv subjects

Marion Moore Campisi

Publications and source records attributed to Marion Moore Campisi.

2 recordsLinked to original sources

arXiv2011

alpha-sloped Generalized Heegaard splittings of 3-manifolds

We generalize the definition of thin position of Scharlemann and Thompson for compact orientable 3-manifolds with torus boundary components and introduce $α$-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.

math.GT↗

arXiv2010

High distance knots in closed 3-manifolds

Let M be a closed 3-manifold with a given Heegaard splitting. We show that after a single stabilization, some core of the stabilized splitting has arbitrarily high distance with respect to the splitting surface. This generalizes a result of Minsky, Moriah, and Schleimer for knots in S^3. We also show that in the complex of curves, handlebody sets are either coarsely distinct or identical. We define the coarse mapping class group of a Heeegaard splitting, and show that if (S, V, W) is a Heegaard splitting of genus greater than or equal to 2, then the coarse mapping class group of (S,V,W) is isomorphic to the mapping class group of (S, V,W).

math.GT↗