Deck Transformations and Group Actions 70. Additional Topics
نویسنده
چکیده
منابع مشابه
Characterization of Non-minimal Tree Actions
Let Γ be a group acting without inversions on a tree X. If there is no proper Γ-invariant subtree, we call the action of Γ on X minimal. Here we give a characterization of non-minimal tree actions. For a non-minimal action of Γ on X, we give structure theorems for the quotient graph of groups for Γ on X, its associated edge-indexed graph and its group of deck transformations.
متن کاملAlgebraic Topology (hatcher)
Part 1. The Fundamental Group 3 2. Basic Constructions 3 2.1. Paths and Homotopy 3 2.2. The Fundamental Group of the Circle 4 2.3. Induced Homomorphisms 6 3. Van Kampen’s Theorem 7 3.1. Free Products of Groups 7 3.2. The Van Kampen Theorem 7 3.3. Application to Cell Complexes 9 4. Covering Spaces 11 4.1. Lifting Properties 11 4.2. The Classification of Covering Spaces 12 4.3. Deck Transformatio...
متن کاملPerfect Shuffles and Affine Groups
For positive integers k and n the group of perfect k-shuffles with a deck of kn cards is a subgroup of the symmetric group Skn. The structure of these groups was found for k = 2 by Diaconis, Graham, and Kantor and for k ≥ 3 and a deck of km cards by Medvedoff and Morrison. They also conjectured that for k = 4 and deck size 2m, m odd, the group is isomorphic to the group of affine transformation...
متن کاملAddendum to: "Infinite-dimensional versions of the primary, cyclic and Jordan decompositions", by M. Radjabalipour
In his paper mentioned in the title, which appears in the same issue of this journal, Mehdi Radjabalipour derives the cyclic decomposition of an algebraic linear transformation. A more general structure theory for linear transformations appears in Irving Kaplansky's lovely 1954 book on infinite abelian groups. We present a translation of Kaplansky's results for abelian groups into the terminolo...
متن کاملPlatonic polyhedra tune the 3 - sphere : Harmonic analysis on simplices . Peter Kramer
A spherical topological manifold of dimension n − 1 forms a prototile on its cover, the (n-1)-sphere. The tiling is generated by the fixpoint-free action of the group of deck transformations. By a general theorem, this group is isomorphic to the first homotopy group. Multiplicity and selection rules appear in the form of reduction of group representations. A basis for the harmonic analysis on t...
متن کامل