Tessellations of solvmanifolds
Copyright policy )Tessellations of solvmanifolds
Let A A be a closed subgroup of a connected, solvable Lie group G G , such that the homogeneous space A ∖ G A\backslash G is simply connected. As a special case of a theorem of C. T. C. Wall, it is known that every tessellation A ∖ G / Γ A\backslash G/\Gamma of A ∖ G A\backslash G is finitely covered by a compact homogeneous space G ′ / Γ ′ G’/\Gamma ’ . We prove that the covering map can be taken to be very well behaved — a “crossed" affine map. This establishes a connection between the geometry of the tessellation and the geometry of the homogeneous space. In particular, we see that every geometrically-defined flow on A ∖ G / Γ A\backslash G/\Gamma that has a dense orbit is covered by a natural flow on G ′ / Γ ′ G’/\Gamma ’ .
- Amridge University United States
- Williams College United States
- Oklahoma State University Oklahoma City United States
- Oklahoma State University–Stillwater United States
Discontinuous groups of transformations, Other geometric groups, including crystallographic groups, Nilpotent and solvable Lie groups, solvmanifold, Discrete subgroups of Lie groups, solvtessellation, geometric flow, solvable Lie group, Differential geometry of homogeneous manifolds, nilshadow, Combinatorial aspects of tessellation and tiling problems, Linear algebraic groups over the reals, the complexes, the quaternions, nilmanifold, Noncompact Lie groups of transformations, syndetic hull
Discontinuous groups of transformations, Other geometric groups, including crystallographic groups, Nilpotent and solvable Lie groups, solvmanifold, Discrete subgroups of Lie groups, solvtessellation, geometric flow, solvable Lie group, Differential geometry of homogeneous manifolds, nilshadow, Combinatorial aspects of tessellation and tiling problems, Linear algebraic groups over the reals, the complexes, the quaternions, nilmanifold, Noncompact Lie groups of transformations, syndetic hull
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