14 research outputs found
Polish Topologies for Graph Products of Cyclic Groups
We give a complete characterization of the graph products of cyclic groups
admitting a Polish group topology, and show that they are all realizable as the
group of automorphisms of a countable structure. In particular, we characterize
the right-angled Coxeter groups (resp. Artin groups) admitting a Polish group
topology. This generalizes results from [5], [7] and [4]
Polish Topologies for Graph Products of Groups
We give strong necessary conditions on the admissibility of a Polish group
topology for an arbitrary graph product of groups , and use
them to give a characterization modulo a finite set of nodes. As a corollary,
we give a complete characterization in case all the factor groups are
countable
No Uncountable Polish Group Can be a Right-Angled Artin Group
We prove that if G is a Polish group and A a group admitting a system of generators whose associated length function satisfies: (i) if 0 < k < ω , then l g ( x ) ≤ l g ( x k ) ; (ii) if l g ( y ) < k < ω and x k = y , then x = e , then there exists a subgroup G * of G of size b (the bounding number) such that G * is not embeddable in A. In particular, we prove that the automorphism group of a countable structure cannot be an uncountable right-angled Artin group. This generalizes analogous results for free and free abelian uncountable groups
Quantization of two types of Multisymplectic manifolds
This thesis is concerned with quantization of two types of multisymplectic manifolds that have multisymplectic forms coming from a Kahler form. In chapter 2 we show that in both cases they can be quantized using Berezin-Toeplitz quantization and that the quantizations have reasonable semiclassical properties.
In the last chapter of this work, we obtain two additional results. The first concerns the deformation quantization of the (2n-1)-plectic structure that we examine in chapter 2, we make the first step toward the definition of a star product on the Nambu-Poisson algebra (C^{\infty}(M),{.,...,.}). The second result concerns the algebraic properties of the generalized commutator
Multicoloured Random Graphs: Constructions and Symmetry
This is a research monograph on constructions of and group actions on
countable homogeneous graphs, concentrating particularly on the simple random
graph and its edge-coloured variants. We study various aspects of the graphs,
but the emphasis is on understanding those groups that are supported by these
graphs together with links with other structures such as lattices, topologies
and filters, rings and algebras, metric spaces, sets and models, Moufang loops
and monoids. The large amount of background material included serves as an
introduction to the theories that are used to produce the new results. The
large number of references should help in making this a resource for anyone
interested in beginning research in this or allied fields.Comment: Index added in v2. This is the first of 3 documents; the other 2 will
appear in physic