2015/05/19 by Ekaterina Pervova, Pervova, Ekaterina
Mathematics · #53C15 (primary) #57R35 (secondary) #Advanced Topics in Algebra #Differential Geometry (math.DG) #FOS: Mathematics #Geometric and Algebraic Topology #Group Theory (math.GR) #Homotopy and Cohomology in Algebraic Topology
paper · pdf · doi:10.48550/arxiv.1505.04915
openalex publication_date 2015/05/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We consider certain groups of tree automorphisms as so-called diffeological groups. The notion of diffeology, due to Souriau, allows to endow non-manifold topological spaces, such as regular trees that we look at, with a kind of a differentiable structure that in many ways is close to that of a smooth manifold; a suitable notion of a diffeological group follows. We first study the question of what kind of a diffeological structure is the most natural to put on a regular tree in a way that the underlying topology be the standard one of the tree. We then proceed to consider the group of all automorphisms of the tree as a diffeological space, with respect to the functional diffeology, showing that this diffeology is actually the discrete one, the fact that therefore is true for its subgroups as well.