- In mathematics, an
atoroidal 3-manifold is one that does not
contain an
essential torus.
There are two
major variations in this terminology: an essential...
-
subject of
geometric group theory, an
acylindrically hyperbolic group is a
group admitting a non-elementary '
acylindrical'
isometric action on some geodesic...
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discontinuity of the action. A
group is said to be
acylindrically hyperbolic if it
admits a non-elementary
acylindrical action on a (not
necessarily proper) Gromov-hyperbolic...
-
uniformly on a cube,
tetrahedron or
other Platonic solid. Similarly, the
acylindricity c {\displaystyle c} is
defined by c = d e f λ y 2 − λ x 2 {\displaystyle...
- Gromov-hyperbolic
groups and
their generalizations (relatively and
acylindrically hyperbolic groups), free
groups and
their automorphisms,
groups acting...
-
William Thurston,
Hyperbolic structures on 3-manifolds. I.
Deformation of
acylindrical manifolds. Ann. of Math. (2) 124 (1986), no. 2, 203–246.
William Thurston...
- particular, all
groups that do not
contain non-abelian free subgroups);
Acylindrical accessibility results for
finitely presented (Sela, Delzant) and finitely...
-
hyperbolic manifolds of
finite volume.
Further generalizations such as
acylindrical hyperbolicity are also
explored by
current research. Just like Gromov-hyperbolic...
-
faces of a bar
composed of 5
laser diodes, can be
imaged by
means of 4 (
acylindrical)
cylinder lenses onto an
image plane with 5
spots each with a size of...
-
starting with "Hyperbolic
structures on 3-manifolds. I.
Deformation of
acylindrical manifolds" (Ann. of Math. (2) 124 (1986), no. 2, 203–246), that revolutionized...
