1,721,002 research outputs found
Structure theorems for subgroups of homeomorphism groups
No full textLet Homeo(S1) represent the full group of homeomorphisms of the unit circle S1, and let A represent the set of subgroups of Homeo(S1) satisfying the two properties that if G ? A then 1) G contains only orientation preserving homeomorphisms of S1 and 2) G contains no non-abelian free subgroups. This expository article uses classical results about homeomorphisms of the circle and elementary dynamical methods to derive various new and old results about the groups in A; we give a general structure theorem for such groups within a family of such results by Beklaryan, Malyutin, and Solodov, a new proof of Margulis’ Theorem that given G ? A the circle S1 admits a G-invariant probability measure, and we classify the solvable subgroups of R. Thompson’s group T
Some embeddings between symmetric R. Thompson groups
Full text linkFunding: The first author wants to acknowledge financial support from the Spanish Ministry of Economy and Competitiveness, through the “Severo Ochoa Program for Centres of Excellence in R&D” (SEV-2015-0554). The second author wishes to acknowledge support from EPSRC grant EP/R032866/1 during the creation of this paper.Let m ≤ n ∈ ℕ, and G ≤ Sym(m) and H ≤ Sym(n). In this article we find conditions enabling embeddings between the symmetric R. Thompson groups Vm(G) and Vn(H). When n ≡1 mod (m −1), and under some other technical conditions, we find an embedding of Vn(H) into Vm(G) via topological conjugation. With the same modular condition we also generalise a purely algebraic construction of Birget from 2019 to find a group H ≤ Sym(n) and an embedding of Vm(G) into Vn(H).Peer reviewe
An algebraic classification of some solvable groups of homeomorphisms
No full textAbstractWe produce two separate algebraic descriptions of the isomorphism classes of the solvable subgroups of the group PLo(I) of piecewise-linear orientation-preserving homeomorphisms of the unit interval under the operation of composition, and also of the generalized R. Thompson groups Fn. The first description is as a set of isomorphism classes of groups which is closed under three algebraic operations, and the second is as the set of isomorphism classes of subgroups of a countable collection of easily described groups. We show the two descriptions are equivalent
Cayley automaton semigroups
No full textLet S be a semigroup, C(S) the automaton constructed from the right Cayley
graph of S with respect to all of S as the generating set and ∑(C(S)) the
automaton semigroup constructed from C(S). Such semigroups are termed
Cayley automaton semigroups. For a given semigroup S we aim to establish
connections between S and ∑(C(S)).
For a finite monogenic semigroup S with a non-trivial cyclic subgroup C[sub]n we
show that ∑(C(S)) is a small extension of a free semigroup of rank n, and
that in the case of a trivial subgroup ∑(C(S)) is finite.
The notion of invariance is considered and we examine those semigroups S
satisfying S ≅ ∑(C(S)). We classify which bands satisfy this, showing that
they are those bands with faithful left-regular representations, but exhibit
examples outwith this classification. In doing so we answer an open problem
of Cain.
Following this, we consider iterations of the construction and show that for
any n there exists a semigroup where we can iterate the construction n times
before reaching a semigroup satisfying S ≅ ∑(C(S)). We also give an example of a semigroup where repeated iteration never produces a semigroup
satisfying S ≅ ∑(C(S)).
Cayley automaton semigroups of infinite semigroups are also considered and
we generalise and extend a result of Silva and Steinberg to cancellative semigroups. We also construct the Cayley automaton semigroup of the bicyclic
monoid, showing in particular that it is not finitely generated
Constructing 2-generated subgroups of the group of homeomorphisms of Cantor space
No full textWe study finite generation, 2-generation and simplicity of subgroups of H[sub]c, the
group of homeomorphisms of Cantor space.
In Chapter 1 and Chapter 2 we run through foundational concepts and notation. In Chapter 3 we study vigorous subgroups of H[sub]c. A subgroup G of H[sub]c is vigorous if for any non-empty clopen set A with proper non-empty clopen subsets B and C there exists g ∈ G with supp(g) ⊑ A and Bg ⊆ C. It is a corollary of the main theorem of Chapter 3 that all finitely generated simple vigorous subgroups of H[sub]c are in fact 2-generated. We show the family of finitely generated, simple, vigorous subgroups of H[sub]c is closed under several natural constructions.
In Chapter 4 we use a generalised notion of word and the tight completion construction from [13] to construct a family of subgroups of H[sub]c which generalise Thompson's group V . We give necessary conditions for these groups to be finitely generated and simple. Of these we show which are vigorous. Finally we give some examples
Going Beyond Counting First Authors in Author Co-citation Analysis
Full text linkThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
Fractal, group theoretic, and relational structures on Cantor space
No full textCantor space, the set of infinite words over a finite alphabet, is a type of metric space
with a `self-similar' structure. This thesis explores three areas concerning Cantor space
with regard to fractal geometry, group theory, and topology.
We find first results on the dimension of intersections of fractal sets within the Cantor
space. More specifically, we examine the intersection of a subset E of the n-ary Cantor
space, C[sub]n with the image of another subset Funder a random isometry. We obtain
almost sure upper bounds for the Hausdorff and upper box-counting dimensions of the
intersection, and a lower bound for the essential supremum of the Hausdorff dimension.
We then consider a class of groups, denoted by V[sub]n(G), of homeomorphisms of the
Cantor space built from transducers. These groups can be seen as homeomorphisms
that respect the self-similar and symmetric structure of C[sub]n, and are supergroups of the
Higman-Thompson groups V[sub]n. We explore their isomorphism classes with our primary
result being that V[sub]n(G) is isomorphic to (and conjugate to) V[sub]n if and only if G is a
semiregular subgroup of the symmetric group on n points.
Lastly, we explore invariant relations on Cantor space, which have quotients homeomorphic to fractals in many different classes. We generalize a method of describing these
quotients by invariant relations as an inverse limit, before characterizing a specific class
of fractals known as Sierpiński relatives as invariant factors. We then compare relations
arising through edge replacement systems to invariant relations, detailing the conditions
under which they are the same
Variations on the Author
Full text link“Variations on the Author” discusses two of Eduardo Coutinho’s recent films (Um Dia na Vida, from 2010, and Últimas Conversas, posthumously released in 2015) and their contribution to the general question of documentary authorship. The director’s filmography is characterized by a consistent yet self-effacing form of authorial self-inscription: Coutinho often features as an interviewer that rather than express opinions propels discourses; an interviewer that is good at listening. This mode of self-inscription characterizes him as an author who is not expressive but who is nonetheless markedly present on the screen. In Um Dia na Vida, however, Coutinho is completely absent form the image, while Últimas Conversas, on the contrary, includes a confessional prologue that moves the director from the margins to the center of his films. This article examines the ways in which these works stand out in the filmography of a director who offers new insights into the notion of cinematic authorship
Appropriate Similarity Measures for Author Cocitation Analysis
Full text linkWe provide a number of new insights into the methodological discussion about author cocitation analysis. We first argue that the use of the Pearson correlation for measuring the similarity between authors’ cocitation profiles is not very satisfactory. We then discuss what kind of similarity measures may be used as an alternative to the Pearson correlation. We consider three similarity measures in particular. One is the well-known cosine. The other two similarity measures have not been used before in the bibliometric literature. Finally, we show by means of an example that our findings have a high practical relevance.information science;Pearson correlation;cosine;similarity measure;author cocitation analysis
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