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math.GT2021★ 1 cited
Computing a Link Diagram from its Exterior
Nathan M. Dunfield, Malik Obeidin, Cameron Gates Rudd
A knot is a circle piecewise-linearly embedded into the 3-sphere. The topology of a knot is intimately related to that of its exterior, which is the complement of an open regular n…
math.GT2021
Stable Isoperimetric Ratios and the Hodge Laplacian of Hyperbolic Manifolds
Cameron Gates Rudd
We show that for a closed hyperbolic 3-manifold the size of the first eigenvalue of the Hodge Laplacian acting on coexact 1-forms is comparable to an isoperimetric ratio relating g…