100 research outputs found
On the simplicity of homeomorphism groups of a tilable lamination
We show that the identity component of the group of homeomorphisms that
preserve all leaves of a R^d-tilable lamination is simple. Moreover, in the one
dimensional case, we show that this group is uniformly perfect. We obtain a
similar result for a dense subgroup of homeomorphisms.Comment: 14
Darboux cyclides and webs from circles
Motivated by potential applications in architecture, we study Darboux
cyclides. These algebraic surfaces of order a most 4 are a superset of Dupin
cyclides and quadrics, and they carry up to six real families of circles.
Revisiting the classical approach to these surfaces based on the spherical
model of 3D Moebius geometry, we provide computational tools for the
identification of circle families on a given cyclide and for the direct design
of those. In particular, we show that certain triples of circle families may be
arranged as so-called hexagonal webs, and we provide a complete classification
of all possible hexagonal webs of circles on Darboux cyclides.Comment: 34 pages, 20 figure
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