Topology of plane sections of periodic polyhedra with an application to the truncated octahedron.

We give a Thurston classification of those bicritical rational maps which have two period two superattracting cycles. We also show that all such maps are constructed by the mating of two unicritical degree $d$ polynomials.

Special positions for surfaces bounded by closed braids.

Lee Rudolph (1985)

Revista Matemática Iberoamericana

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Captures, matings and regluings

Inna Mashanova, Vladlen Timorin (2012)

Annales de la faculté des sciences de Toulouse Mathématiques

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In parameter slices of quadratic rational functions, we identify arcs represented by matings of quadratic polynomials. These arcs are on the boundaries of hyperbolic components.

Some examples of essential laminations in 3-manifolds

Allen Hatcher (1992)

Annales de l'institut Fourier

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Families of codimension-one foliations and laminations are constructed in certain 3-manifolds, with the property that their transverse intersection with the boundary torus of the manifold consists of parallel curves whose slope varies continuously with certain parameters in the construction. The 3-manifolds are 2-bridge knot complements and punctured-torus bundles.

On singularities of capillary surfaces in the absence of gravity.

Roytburd, V. (1983)

International Journal of Mathematics and Mathematical Sciences

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