Finite domination and Novikov rings: Laurent polynomial rings in two variables

Let C be a bounded cochain complex of finitely generatedfree modules over the Laurent polynomial ring L = R[x, x−1, y, y−1].The complex C is called R-finitely dominated if it is homotopy equivalentover R to a bounded complex of finitely generated projective Rmodules.Our main result characterises R-finitely dominated complexesin terms of Novikov cohomology: C is R-finitely dominated if andonly if eight complexes derived from C are acyclic; these complexes areC ⊗L R[[x, y]][(xy)−1] and C ⊗L R[x, x−1][[y]][y−1], and their variants obtainedby swapping x and y, and replacing either indeterminate by its inverse.

Coping with emotional labour in tennis coaching

A tennis coach works in a social environment, employed in a service based economy with the outcome of client-customer interactions significantly impacting on the consumer experience. Research conducted outside of sport has shown that positive affective displays during interactions, which in a tennis situation may include providing support through displays of warmth, empathy, positivity and compassion as the client attempts to master a new technique, have shown positive associations with customer satisfaction. Hochschild (1983) coined the term ‘emotional labour’ to describe the process of, and demands resulting from adjusting one’s demeanour, language and tone during social encounters in a planned and strategic manner in order to facilitate a positive outcome. Hochschild proposed that individuals in jobs which require a high degree of face-to-face interaction with the public are particularly at risk of experiencing potentially deleterious effects that result from dealing with emotional labour demands on a daily basis. It would appear that tennis coaches work in environments that make them susceptible to experiencing emotional labour and as such the intention of this article is to first introduce the concept and then to provide suggestions for how a coach may cope with these demands.

Variétés de drapeaux et opérateurs différentiels

Soit G un groupe algébrique semi-simple sur un corps de caractéristique 0. Ce mémoire discute d'un théorème d'annulation de la cohomologie supérieure du faisceau D des opérateurs différentiels sur une variété de drapeaux de G. On démontre que si P est un sous-groupe parabolique de G, alors H^i(G/P,D)=0 pour tout i>0. On donne en fait trois preuves indépendantes de ce théorème. La première preuve est de Hesselink et n'est valide que dans le cas où le sous-groupe parabolique est un sous-groupe de Borel. Elle utilise un argument de suites spectrales et le théorème de Borel-Weil-Bott. La seconde preuve est de Kempf et n'est valide que dans le cas où le radical unipotent de P agit trivialement sur son algèbre de Lie. Elle n'utilise que le théorème de Borel-Weil-Bott. Enfin, la troisième preuve est attribuée à Elkik. Elle est valide pour tout sous-groupe parabolique mais utilise le théorème de Grauert-Riemenschneider. On présente aussi une construction détaillée du faisceau des opérateurs différentiels sur une variété.

Le théorème de Borel-Weil-Bott

Mémoire numérisé par la Division de la gestion de documents et des archives de l'Université de Montréal

Cohomologie de fibrés en droite sur le fibré cotangent de variétés grassmanniennes généralisées

Cette thèse s'intéresse à la cohomologie de fibrés en droite sur le fibré cotangent de variétés projectives. Plus précisément, pour $G$ un groupe algébrique simple, connexe et simplement connexe, $P$ un sous-groupe maximal de $G$ et $\omega$ un générateur dominant du groupe de caractères de $P$, on cherche à comprendre les groupes de cohomologie $H^i(T^*(G/P),\mathcal{L})$ où $\mathcal{L}$ est le faisceau des sections d'un fibré en droite sur $T^*(G/P)$. Sous certaines conditions, nous allons montrer qu'il existe un isomorphisme, à graduation près, entre $H^i(T^*(G/P),\mathcal{L})$ et $H^i(T^*(G/P),\mathcal{L}^{\vee})$ Après avoir travaillé dans un contexte théorique, nous nous intéresserons à certains sous-groupes paraboliques en lien avec les orbites nilpotentes. Dans ce cas, l'algèbre de Lie du radical unipotent de $P$, que nous noterons $\nLie$, a une structure d'espace vectoriel préhomogène. Nous pourrons alors déterminer quels cas vérifient les hypothèses nécessaires à la preuve de l'isomorphisme en montrant l'existence d'un $P$-covariant $f$ dans $\comp[\nLie]$ et en étudiant ses propriétés. Nous nous intéresserons ensuite aux singularités de la variété affine $V(f)$. Nous serons en mesure de montrer que sa normalisation est à singularités rationnelles.

Fourier-Matrizen und Ringe mit Basis

Bei der Bestimmung der irreduziblen Charaktere einer Gruppe vom Lie-Typ entwickelte Lusztig eine Theorie, in der eine sogenannte Fourier-Transformation auftaucht. Dies ist eine Matrix, die nur von der Weylgruppe der Gruppe vom Lie-Typ abhängt. Anhand der Eigenschaften, die eine solche Fourier- Matrix erfüllen muß, haben Geck und Malle ein Axiomensystem aufgestellt. Dieses ermöglichte es Broue, Malle und Michel füur die Spetses, über die noch vieles unbekannt ist, Fourier-Matrizen zu bestimmen. Das Ziel dieser Arbeit ist eine Untersuchung und neue Interpretation dieser Fourier-Matrizen, die hoffentlich weitere Informationen zu den Spetses liefert. Die Werkzeuge, die dabei entstehen, sind sehr vielseitig verwendbar, denn diese Matrizen entsprechen gewissen Z-Algebren, die im Wesentlichen die Eigenschaften von Tafelalgebren besitzen. Diese spielen in der Darstellungstheorie eine wichtige Rolle, weil z.B. Darstellungsringe Tafelalgebren sind. In der Theorie der Kac-Moody-Algebren gibt es die sogenannte Kac-Peterson-Matrix, die auch die Eigenschaften unserer Fourier-Matrizen besitzt. Ein wichtiges Resultat dieser Arbeit ist, daß die Fourier-Matrizen, die G. Malle zu den imprimitiven komplexen Spiegelungsgruppen definiert, die Eigenschaft besitzen, daß die Strukturkonstanten der zugehörigen Algebren ganze Zahlen sind. Dazu müssen äußere Produkte von Gruppenringen von zyklischen Gruppen untersucht werden. Außerdem gibt es einen Zusammenhang zu den Kac-Peterson-Matrizen: Wir beweisen, daß wir durch Bildung äußerer Produkte von den Matrizen vom Typ A(1)1 zu denen vom Typ C(1) l gelangen. Lusztig erkannte, daß manche seiner Fourier-Matrizen zum Darstellungsring des Quantendoppels einer endlichen Gruppe gehören. Deswegen ist es naheliegend zu versuchen, die noch ungeklärten Matrizen als solche zu identifizieren. Coste, Gannon und Ruelle untersuchen diesen Darstellungsring. Sie stellen eine Reihe von wichtigen Fragen. Eine dieser Fragen beantworten wir, nämlich inwieweit rekonstruiert werden kann, zu welcher endlichen Gruppe gegebene Matrizen gehören. Den Darstellungsring des getwisteten Quantendoppels berechnen wir für viele Beispiele am Computer. Dazu müssen unter anderem Elemente aus der dritten Kohomologie-Gruppe H3(G,C×) explizit berechnet werden, was bisher anscheinend in noch keinem Computeralgebra-System implementiert wurde. Leider ergibt sich hierbei kein Zusammenhang zu den von Spetses herrührenden Matrizen. Die Werkzeuge, die in der Arbeit entwickelt werden, ermöglichen eine strukturelle Zerlegung der Z-Ringe mit Basis in bekannte Anteile. So können wir für die meisten Matrizen der Spetses Konstruktionen angeben: Die zugehörigen Z-Algebren sind Faktorringe von Tensorprodukten von affinen Ringe Charakterringen und von Darstellungsringen von Quantendoppeln.

Global analytic regularity for structures of co-rank one

We consider real analytic involutive structures V, of co-rank one, defined on a real analytic paracompact orientable manifold M. To each such structure we associate certain connected subsets of M which we call the level sets of V. We prove that analytic regularity propagates along them. With a further assumption on the level sets of V we characterize the global analytic hypoellipticity of a differential operator naturally associated to V. As an application we study a case of tube structures.

Star products made (somewhat) easier

We develop an approach to the deformation quantization on the real plane with an arbitrary Poisson structure which is based on Weyl symmetrically ordered operator products. By using a polydifferential representation for the deformed coordinates, xj we are able to formulate a simple and effective iterative procedure which allowed us to calculate the fourth-order star product (and may be extended to the fifth order at the expense of tedious but otherwise straightforward calculations). Modulo some cohomology issues which we do not consider here, the method gives an explicit and physics-friendly description of the star products.

ABELIANIZED OBSTRUCTION FOR FIXED POINTS OF FIBER-PRESERVING MAPS OF SURFACE BUNDLES

Let f: M -> M be a fiber-preserving map where S -> M -> B is a bundle and S is a closed surface. We study the abelianized obstruction, which is a cohomology class in dimension 2, to deform f to a fixed point free map by a fiber-preserving homotopy. The vanishing of this obstruction is only a necessary condition in order to have such deformation, but in some cases it is sufficient. We describe this obstruction and we prove that the vanishing of this class is equivalent to the existence of solution of a system of equations over a certain group ring with coefficients given by Fox derivatives.

On cohomologies and extensions of cyclic groups

Cohomology groups H(s)(Z(n), Z(m)) are studied to describe all groups up to isomorphism which are (central) extensions of the cyclic group Z(n) by the Z(n)-module Z(m). Further, for each such a group the number of non-equivalent extensions is determined. (C) 2011 Elsevier B.V. All rights reserved.

Automorphism Groups of Generalized (Binary) Icosahedral, Tetrahedral and Octahedral Groups

Let G be any of the (binary) icosahedral, generalized octahedral (tetrahedral) groups or their quotients by the center. We calculate the automorphism group Aut(G).

Spherical space forms - Homotopy self-equivalences and homotopy types, the case of the groups Z/a x (Z/b x TL(2)(F(p)))

Let G = Z/a x(mu) (Z/b x TL(2)(F(p))) and X(n) be an n-dimensional CW-complex with the homotopy type of the n-sphere. We determine the automorphism group Aut(G) and then compute the number of distinct homotopy types of spherical space forms with respect to free and cellular G-actions on all CW-complexes X(2dn - 1), where 2d is a period of G. Next, the group E(X(2dn - 1)/alpha) of homotopy self-equivalences of spherical space forms X(2dn - 1)/alpha, associated with such G-actions alpha on X(2dn - 1) are studied. Similar results for the rest of finite periodic groups have been obtained recently and they are described in the introduction. (C) 2009 Elsevier B.V. All rights reserved.

Att möta sorg i arbetet : En kvantitativ enkätundersökning över begravningsrådgivare anslutna till SBF (Sveriges Begravningsbyråers Förbund).

This quantitative survey aims to highlight the impact of the meeting with the grief for customer advisers and representatives of funeral homes connected to the SBF (Sveriges Begravningsbyråers förbund). It also aims to demonstrate any differences between the sexes on this subject. Issues include: How does the person experience expectations and requirements in relation to their professional role? Does the person experience a personal impact due to the encounter with grief and death in their profession, in what way and to what extent? What consequences does the expectations, reactions and the possible impact result in for that person? What conditions does the person have to help cope with the professional role? Is there a gender difference in this experience? The theory base, which consists of theories taken from The Managed Heart: The commercialization of Human Feeling by Arlie Hochschild (2003) and descriptions taken from Yrke: begravningsentreprenör. Om utanförskap, döda kroppar, riter och professionalisering by Anna Davidsson Bremborg (2002), has been fundamental in both the preparatory work and the analysis. The population consists of those with client contact at funeral homes connected to the SBF. The questionnaire was answered through an internet page and the contact with the particiants were made via e-mail. The questionnaire consisted of 44 claims which were answered by how well the respondents agreed with them. The responses were then coded and calculations were made of mean and significance of these figures. Comparisons were made on several levels between the different variables in order to find patterns and indications. The results showed trends that the respondents to some extent experienced high demands in their profession, stress connected with the customer interactions and that this to some extent resulted in negative consequences. The results suggests that respondents were expected to and strove to go the "extra mile" to please the customers. The results also showed trends that the respondents enjoyed their work, experienced relatively good conditions in their profession and that the benefits outweighed the sacrifices. The results also showed an interesting pattern of that women, more than men, experience pressures and stress due to the encouter with grief at work, and that the higher education the respondents had the greater the impact. This study resulted in some interesting indications that can be used in further research.

Feeling in sociology and the world

Sociologisk Forsknings digitala arkiv

Loja de experiência, trabalho emocional e consumo: o trabalho dos vendedores e gerente da loja para a transmissão da experiência da marca Chilli Beans

O objetivo desta dissertação é compreender a forma como se estrutura o trabalho dos vendedores e gerente de uma loja de experiência para a transmissão da experiência da marca. O embasamento teórico que deu sustentação à pesquisa aborda discussões sobre o aspecto experiencial do consumo (Holbrook & Hirchsman, 1982b Pine & Gilmore, 2000), experiência da marca (Brakus et al., 2009) e trabalho emocional (Hochschild, 1982; Korczysnki, 2005). Este estudo buscou, através dos métodos shadowing e etnografia de curto prazo, analisar o trabalho dos vendedores e gerente de uma loja de experiência de marca brasileira Chilli Beans, para identificar como estes trabalhadores transmitem a experiência da marca aos consumidores. Os resultados foram coletados durante 45 dias de pesquisa em campo, realizada na loja de experiência da marca Chilli Beans localizada na Rua Oscar Freire, em São Paulo. Ao longo da pesquisa de campo foi possível obter informações sobre a rotina dos trabalhadores, treinamentos, reuniões de avaliação de desempenho e eventos, que proporcionaram a compreensão sobre o trabalho realizado na loja de experiência. Além disso, foram realizadas entrevistas com cinco funcionários da loja, do sexo feminino e masculino, entre 18 e 26 anos, residentes na cidade de São Paulo. Os resultados demonstraram que os trabalhadores utilizam o trabalho emocional para a transmissão da experiência da marca. O trabalho destes vendedores se caracteriza pela busca do atendimento pleno do consumidor, mediante interação emocional, soberania e encantamentos que direcionam o consumidor à aquisição de seus produtos. Para isso, a marca lança mão de treinamentos que objetivam desenvolver as habilidades e técnicas dos vendedores para envolver emocionalmente o consumidor, a fim de direcioná-lo à compra do produto.