1,856 research outputs found
Symplectic fillings of Seifert fibered spaces
We give finiteness results and some classifications up to diffeomorphism of
minimal strong symplectic fillings of Seifert fibered spaces over S^2
satisfying certain conditions, with a fixed natural contact structure. In some
cases we can prove that all symplectic fillings are obtained by rational
blow-downs of a plumbing of spheres. In other cases, we produce new manifolds
with convex symplectic boundary, thus yielding new cut-and-paste operations on
symplectic manifolds containing certain configurations of symplectic spheres.Comment: 39 pages, 21 figures, v2 a few minor corrections and citations, v3
added clarifications in the proof of Lemma 2.8, plus some minor change
Dessins d'enfants for analysts
We present an algorithmic way of exactly computing Belyi functions for
hypermaps and triangulations in genus 0 or 1, and the associated dessins, based
on a numerical iterative approach initialized from a circle packing combined
with subsequent lattice reduction. The main advantage compared to previous
methods is that it is applicable to much larger graphs; we use very little
algebraic geometry, and aim for this paper to be as self-contained as possible
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