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Geometric and combinatorial structure of a class of spherical folding tessellations – I

Catarina P. Avelino, Altino F. Santos (2017)

Czechoslovak Mathematical Journal

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....

Geometric Invariant Theory and Generalized Eigenvalue Problem II

Nicolas Ressayre (2011)

Annales de l’institut Fourier

Let G be a connected reductive subgroup of a complex connected reductive group G ^ . Fix maximal tori and Borel subgroups of G and G ^ . Consider the cone ℒ ℛ ∘ ( G , G ^ ) generated by the pairs ( ν , ν ^ ) of strictly dominant characters such that V ν * is a submodule of V ν ^ . We obtain a bijective parametrization of the faces of ℒ ℛ ∘ ( G , G ^ ) as a consequence of general results on GIT-cones. We show how to read the inclusion of faces off this parametrization.

Geometric subgroups of surface braid groups

Luis Paris, Dale Rolfsen (1999)

Annales de l'institut Fourier

Let M be a surface, let N be a subsurface, and let n ≤ m be two positive integers. The inclusion of N in M gives rise to a homomorphism from the braid group B n N with n strings on N to the braid group B m M with m strings on M . We first determine necessary and sufficient conditions that this homomorphism is injective, and we characterize the commensurator, the normalizer and the centralizer of π 1 N in π 1 M . Then we calculate the commensurator, the normalizer and the centralizer of B n N in B m M for large surface braid...

Geometry of compactifications of locally symmetric spaces

Lizhen Ji, Robert Macpherson (2002)

Annales de l’institut Fourier

For a locally symmetric space M , we define a compactification M ∪ M ( ∞ ) which we call the “geodesic compactification”. It is constructed by adding limit points in M ( ∞ ) to certain geodesics in M . The geodesic compactification arises in other contexts. Two general constructions of Gromov for an ideal boundary of a Riemannian manifold give M ( ∞ ) for locally symmetric spaces. Moreover, M ( ∞ ) has a natural group theoretic construction using the Tits building. The geodesic compactification plays two fundamental roles in...

Global left loop structures on spheres

Michael K. Kinyon (2000)

Commentationes Mathematicae Universitatis Carolinae

On the unit sphere 𝕊 in a real Hilbert space 𝐇 , we derive a binary operation ⊙ such that ( 𝕊 , ⊙ ) is a power-associative Kikkawa left loop with two-sided identity 𝐞 0 , i.e., it has the left inverse, automorphic inverse, and A l properties. The operation ⊙ is compatible with the symmetric space structure of 𝕊 . ( 𝕊 , ⊙ ) is not a loop, and the right translations which fail to be injective are easily characterized. ( 𝕊 , ⊙ ) satisfies the left power alternative and left Bol identities “almost everywhere” but not everywhere....

Currently displaying 121 – 140 of 389