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Signature for piecewise continuous groups
No full textLet be the group of bijections from to itself which are continuous outside a finite set. Let be its quotient by the subgroup of finitely supported permutations. We show that the Kapoudjian class of vanishes. That is, the quotient map splits modulo the alternating subgroup of even permutations. This is shown by constructing a nonzero group homomorphism, called signature, from to . Then we use this signature to list normal subgroups of every subgroup of which contains and such that , the projection of in , is simple
Abelianization of some groups of interval exchanges
Get PDF42 pages, 9 figuresInternational audienceLet IET be the group of bijections from to itself that are continuous outside a finite set, right-continuous and piecewise translations. The abelianization homomorphism , called SAF-homomorphism, was described by Arnoux-Fathi and Sah. The abelian group is the second exterior power of the reals over the rationals. For every subgroup of we define as the subgroup of consisting of all elements such that is continuous outside . Let be the preimage of in . We establish an isomorphism between the abelianization of and the second skew-symmetric power of over denoted by . This group often has non-trivial -torsion, which is not detected by the SAF-homomorphism. We then define the group of all interval exchange transformations with flips. Arnoux proved that this group is simple thus perfect. However for every subgroup we establish an isomorphism between its abelianization and which is a -elementary abelian subgroup of
Invariants of some groups of dynamic origin
No full textLe but de cette thèse est d'étudier des groupes agissant par isométries par morceaux sur un intervalle en s'intéressant à leur abélianisé. Le cas du groupe des échanges d'intervalles IET a été traité par Arnoux-Fathi et Sah. Tout d'abord, pour tous sous-groupe H du groupe des réels, on identifie l'abélianisé de tous les sous-groupes IET(H) du groupe IET. On réalise similairement le cas des sous-groupes de cette forme du groupe des échanges d'intervalles avec renversements. L'idée est adapter le morphisme signature sur les groupes de permutations finis en essayant de mesurer l'ensemble des inversions d'un élément. Par ailleurs on démontre aussi que la signature des groupes des permutations finis s'étend au groupe des permutations de de [0,1[ qui sont continus en dehors d'un nombre fini de points. Cela a pour conséquence que la classe de Kapoudjian, un élément du second groupe de cohomologie, s'annule. Ensuite, on se place en dimension d plus grande ou égale que 1 et on considère le groupe REC des permutations du rectangle unité en dimension d, qui bougent un nombre fini de sous-rectangles par translations et qui sont l'identité ailleurs. On démontre que la généralisation naturel des rotations restreintes (qui forment un système de générateur du groupe IET) forme un système générateur de REC. Puis on identifie son abélianisé en généralisant le travail fait pour le groupe IET par Arnoux-Fathi et Sah.In this thesis we study groups piecewise acting by isometries on an interval by identifying their abelianization. The case of the Interval Exchange Transformations group, IET, has been done by Arnoux-Fathi and Sah. First, for every subgroup H of the reals, we identify the abelianization of every subgroup IET(H) of the group IET. SImilarly, we identify the abelianization of subgroups of this form of the Interval Exchange Transformations group with flips. The idea is to adapt the group homomorphism signature on finite permutation groups by measuring the set of inversions of an element.Also we prove that the group homomorphism signature on finite permutation groups can be extended to the group consisting of permutations of [0,1[ which are continuous outside a finite number of points. A consequence is the vanishing of an element of the second cohomology group called the Kapoudjian class.Then, we deal with higher dimension. Let d greater than 1 and let REC be the group of all permutations of the unit rectangle in dimension d, which are a translation on a finite number of subrectangles and is the identiy elsewhere. We prove that the natural generalization of restricted rotations (which define a generating subset of IET) define a generating subset of REC. Next we identify the abelianization of REC by extending the work of Arnoux-Fathi and Sah on IET
Invariants de certains groupes d’origine dynamique
No full textIn this thesis we study groups piecewise acting by isometries on an interval by identifying their abelianization. The case of the Interval Exchange Transformations group, IET, has been done by Arnoux-Fathi and Sah. First, for every subgroup H of the reals, we identify the abelianization of every subgroup IET(H) of the group IET. SImilarly, we identify the abelianization of subgroups of this form of the Interval Exchange Transformations group with flips. The idea is to adapt the group homomorphism signature on finite permutation groups by measuring the set of inversions of an element.Also we prove that the group homomorphism signature on finite permutation groups can be extended to the group consisting of permutations of [0,1[ which are continuous outside a finite number of points. A consequence is the vanishing of an element of the second cohomology group called the Kapoudjian class.Then, we deal with higher dimension. Let d greater than 1 and let REC be the group of all permutations of the unit rectangle in dimension d, which are a translation on a finite number of subrectangles and is the identiy elsewhere. We prove that the natural generalization of restricted rotations (which define a generating subset of IET) define a generating subset of REC. Next we identify the abelianization of REC by extending the work of Arnoux-Fathi and Sah on IET.Le but de cette thèse est d'étudier des groupes agissant par isométries par morceaux sur un intervalle en s'intéressant à leur abélianisé. Le cas du groupe des échanges d'intervalles IET a été traité par Arnoux-Fathi et Sah. Tout d'abord, pour tous sous-groupe H du groupe des réels, on identifie l'abélianisé de tous les sous-groupes IET(H) du groupe IET. On réalise similairement le cas des sous-groupes de cette forme du groupe des échanges d'intervalles avec renversements. L'idée est adapter le morphisme signature sur les groupes de permutations finis en essayant de mesurer l'ensemble des inversions d'un élément. Par ailleurs on démontre aussi que la signature des groupes des permutations finis s'étend au groupe des permutations de de [0,1[ qui sont continus en dehors d'un nombre fini de points. Cela a pour conséquence que la classe de Kapoudjian, un élément du second groupe de cohomologie, s'annule. Ensuite, on se place en dimension d plus grande ou égale que 1 et on considère le groupe REC des permutations du rectangle unité en dimension d, qui bougent un nombre fini de sous-rectangles par translations et qui sont l'identité ailleurs. On démontre que la généralisation naturel des rotations restreintes (qui forment un système de générateur du groupe IET) forme un système générateur de REC. Puis on identifie son abélianisé en généralisant le travail fait pour le groupe IET par Arnoux-Fathi et Sah
Signature for piecewise continuous groups
No full textInternational audienceLet be the group of bijections from to itself which are continuous outside a finite set. Let be its quotient by the subgroup of finitely supported permutations. We show that the Kapoudjian class of vanishes. That is, the quotient map splits modulo the alternating subgroup of even permutations. This is shown by constructing a nonzero group homomorphism, called signature, from to . Then we use this signature to list normal subgroups of every subgroup of which contains and such that , the projection of in , is simple
Invariants de certains groupes d’origine dynamique
No full textIn this thesis we study groups piecewise acting by isometries on an interval by identifying their abelianization. The case of the Interval Exchange Transformations group, IET, has been done by Arnoux-Fathi and Sah. First, for every subgroup H of the reals, we identify the abelianization of every subgroup IET(H) of the group IET. SImilarly, we identify the abelianization of subgroups of this form of the Interval Exchange Transformations group with flips. The idea is to adapt the group homomorphism signature on finite permutation groups by measuring the set of inversions of an element.Also we prove that the group homomorphism signature on finite permutation groups can be extended to the group consisting of permutations of [0,1[ which are continuous outside a finite number of points. A consequence is the vanishing of an element of the second cohomology group called the Kapoudjian class.Then, we deal with higher dimension. Let d greater than 1 and let REC be the group of all permutations of the unit rectangle in dimension d, which are a translation on a finite number of subrectangles and is the identiy elsewhere. We prove that the natural generalization of restricted rotations (which define a generating subset of IET) define a generating subset of REC. Next we identify the abelianization of REC by extending the work of Arnoux-Fathi and Sah on IET.Le but de cette thèse est d'étudier des groupes agissant par isométries par morceaux sur un intervalle en s'intéressant à leur abélianisé. Le cas du groupe des échanges d'intervalles IET a été traité par Arnoux-Fathi et Sah. Tout d'abord, pour tous sous-groupe H du groupe des réels, on identifie l'abélianisé de tous les sous-groupes IET(H) du groupe IET. On réalise similairement le cas des sous-groupes de cette forme du groupe des échanges d'intervalles avec renversements. L'idée est adapter le morphisme signature sur les groupes de permutations finis en essayant de mesurer l'ensemble des inversions d'un élément. Par ailleurs on démontre aussi que la signature des groupes des permutations finis s'étend au groupe des permutations de de [0,1[ qui sont continus en dehors d'un nombre fini de points. Cela a pour conséquence que la classe de Kapoudjian, un élément du second groupe de cohomologie, s'annule. Ensuite, on se place en dimension d plus grande ou égale que 1 et on considère le groupe REC des permutations du rectangle unité en dimension d, qui bougent un nombre fini de sous-rectangles par translations et qui sont l'identité ailleurs. On démontre que la généralisation naturel des rotations restreintes (qui forment un système de générateur du groupe IET) forme un système générateur de REC. Puis on identifie son abélianisé en généralisant le travail fait pour le groupe IET par Arnoux-Fathi et Sah
Going Beyond Counting First Authors in Author Co-citation Analysis
Get PDFThe 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
Variations on the Author
Get PDF“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
Get PDFWe 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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