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A classification of dihedral folding tessellations of the sphere whose prototiles are a kite and an equilateral or isosceles triangle was obtained in recent four papers by Avelino and Santos (2012, 2013, 2014 and 2015). In this paper we extend this classification, presenting all dihedral folding tessellations of the sphere by kites and scalene triangles in which the shorter side of the kite is equal to the longest side of the triangle. Within two possible cases of adjacency, only one will be addressed....
Let be a connected reductive subgroup of a complex connected reductive group . Fix maximal tori and Borel subgroups of and . Consider the cone generated by the pairs of strictly dominant characters such that is a submodule of . We obtain a bijective parametrization of the faces of as a consequence of general results on GIT-cones. We show how to read the inclusion of faces off this parametrization.
Let be a surface, let be a subsurface, and let be two positive integers. The inclusion of in gives rise to a homomorphism from the braid group with strings on to the braid group with strings on . We first determine necessary and sufficient conditions that this homomorphism is injective, and we characterize the commensurator, the normalizer and the centralizer of in . Then we calculate the commensurator, the normalizer and the centralizer of in for large surface braid...
For a locally symmetric space , we define a compactification which
we call the “geodesic compactification”. It is constructed by adding limit points in
to certain geodesics in . The geodesic compactification arises in other
contexts. Two general constructions of Gromov for an ideal boundary of a Riemannian
manifold give for locally symmetric spaces. Moreover, has a
natural group theoretic construction using the Tits building. The geodesic
compactification plays two fundamental roles in...
On the unit sphere in a real Hilbert space , we derive a binary operation such that is a power-associative Kikkawa left loop with two-sided identity , i.e., it has the left inverse, automorphic inverse, and properties. The operation is compatible with the symmetric space structure of . is not a loop, and the right translations which fail to be injective are easily characterized. satisfies the left power alternative and left Bol identities “almost everywhere” but not everywhere....
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