Maximally symmetric trees
نویسنده
چکیده
We characterize the “best” model geometries for the class of virtually free groups, and we show that there is a countable infinity of distinct “best” model geometries in an appropriate sense–these are the maximally symmetric trees. The first theorem gives several equivalent conditions on a bounded valence, cocompact tree T without valence 1 vertices saying that T is maximally symmetric. The second theorem gives general constructions for maximally symmetric trees, showing for instance that every virtually free group has a maximally symmetric tree for a model geometry.
منابع مشابه
Fast Detection and Display of Symmetry in Trees
The automatic construction of good drawings of abstract graphs is a problem of practical importance. Displaying symmetry appears as one of the main criteria for achieving goodness. An expression is obtained for the maximum number of axial symmetries of a tree which can be simultaneously displayed in a single drawing, and an algorithm is presented for constructing such a maximally-symmetric draw...
متن کاملFinding Multiple Maximally Redundant Trees in Linear Time
Redundant trees are directed spanning trees, which provide disjoint paths towards their roots. Therefore, this concept is widely applied in the literature both for providing protection and load sharing. The fastest algorithm can find multiple redundant trees, a pair of them rooted at each vertex, in linear time. Unfortunately, edgeor vertex-redundant trees can only be found in 2-edgeor 2-vertex...
متن کاملSpinor Parallel Propagator and Green’s Function in Maximally Symmetric Spaces
We introduce the spinor parallel propagator for maximally symmetric spaces in any dimension. Then, the Dirac spinor Green’s functions in the maximally symmetric spaces Rn, Sn and Hn are calculated in terms of intrinsic geometric objects. The results are covariant and coordinate-independent. ∗E-mail address: [email protected]
متن کاملDifferential Invariants of Maximally Symmetric Submanifolds
Let G be a Lie group acting smoothly on a manifold M . A closed, nonsingular submanifold S ⊂M is called maximally symmetric if its symmetry subgroup GS ⊂ G has the maximal possible dimension, namely dimGS = dimS, and hence S = GS · z0 is an orbit of GS . Maximally symmetric submanifolds are characterized by the property that all their differential invariants are constant. In this paper, we expl...
متن کاملMaximally symmetric subspace decomposition of the Schwarzschild black hole
The well-known Schwarzschild black hole was first obtained as a stationary, spherically symmetric solution of the Einstein’s vacuum field equations. But until thirty years later, efforts were made for the analytic extension from the exterior area (r > 2GM) to the interior one (r < 2GM). As a contrast to its maximally extension in the Kruskal coordinates, we provide a comoving coordinate system ...
متن کامل