Compact Connected Lie Transformation Groups on Spheres with Low Cohomogeneity, I
Compact Connected Lie Transformation Groups on Spheres with Low Cohomogeneity, I

Author: Eldar Straume

Publisher: American Mathematical Soc.

Published: 1996

Total Pages: 106

ISBN-13: 082180409X

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The cohomogeneity of a transformation group ([italic capitals]G, X) is, by definition, the dimension of its orbit space, [italic]c = dim [italic capitals]X, G. By enlarging this simple numerical invariant, but suitably restricted, one gradually increases the complexity of orbit structures of transformation groups. This is a natural program for classical space forms, which traditionally constitute the first canonical family of testing spaces, due to their unique combination of topological simplicity and abundance in varieties of compact differentiable transformation groups.

Compact Connected Lie Transformation Groups on Spheres with Low Cohomogeneity. II
Compact Connected Lie Transformation Groups on Spheres with Low Cohomogeneity. II

Author: Eldar Straume

Publisher: American Mathematical Soc.

Published: 1997

Total Pages: 90

ISBN-13: 0821804839

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The cohomogeneity of a transformation group ([italic capitals]G, X) is, by definition, the dimension of its orbit space, [italic]c = dim [italic capitals]X, G. We are concerned with the classification of differentiable compact connected Lie transformation groups on (homology) spheres, with [italic]c [less than or equal to symbol] 2, and the main results are summarized in five theorems, A, B, C, D, and E in part I. This paper is part II of the project, and addresses theorems D and E. D examines the orthogonal model from theorem A and orbit structures, while theorem E addresses the existence of "exotic" [italic capital]G-spheres.

Abelian Galois Cohomology of Reductive Groups
Abelian Galois Cohomology of Reductive Groups

Author: Mikhail Borovoi

Publisher: American Mathematical Soc.

Published: 1998

Total Pages: 65

ISBN-13: 0821806505

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In this volume, a new function H 2/ab (K, G) of abelian Galois cohomology is introduced from the category of connected reductive groups G over a field K of characteristic 0 to the category of abelian groups. The abelian Galois cohomology and the abelianization map ab1: H1 (K, G) -- H 2/ab (K, G) are used to give a functorial, almost explicit description of the usual Galois cohomology set H1 (K, G) when K is a number field

Cyclic Phenomena for Composition Operators
Cyclic Phenomena for Composition Operators

Author: Paul Bourdon

Publisher: American Mathematical Soc.

Published: 1997

Total Pages: 122

ISBN-13: 0821806300

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We undertake a systematic study of cyclic phenomena for composition operators. Our work shows that composition operators exhibit strikingly diverse types of cyclic behavior, and it connects this behavior with classical problems involving complex polynomial approximation and analytic functional equations.

A Continuum Limit of the Toda Lattice
A Continuum Limit of the Toda Lattice

Author: Percy Deift

Publisher: American Mathematical Soc.

Published: 1998

Total Pages: 233

ISBN-13: 0821806912

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In this book, the authors describe a continuum limit of the Toda ODE system, obtained by taking as initial data for the finite lattice successively finer discretizations of two smooth functions. Using the integrability of the finite Toda lattice, the authors adapt the method introduced by Lax and Levermore for the study of the small dispersion limit of the Korteweg de Vries equations to the case of the Toda lattice. A general class of initial data is considered which permits, in particular, the formation of shocks. A feature of the analysis in this book is an extensive use of techniques from the theory of Riemann-Hilbert problems.

CR-Geometry and Deformations of Isolated Singularities
CR-Geometry and Deformations of Isolated Singularities

Author: Ragnar-Olaf Buchweitz

Publisher: American Mathematical Soc.

Published: 1997

Total Pages: 111

ISBN-13: 082180541X

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In this power we show how to compute the parameter space [italic capital]X for the versal deformation of an isolated singularity ([italic capital]V, 0) under the assumptions [italic]dim [italic capital]V [greater than or equal to symbol] 4, depth {0} [italic capital]V [greater than or equal to symbol] 3, from the CR-structure on a link [italic capital]M of the singularity. We do this by showing that the space [italic capital]X is isomorphic to the space (denoted here by [script capital]K[subscript italic capital]M) associated to [italic capital]M by Kuranishi in 1977. In fact we produce isomorphisms of the associated complete local rings by producing quasi-isomorphisms of the controlling differential graded Lie algebras for the corresponding formal deformation theories.

The Study of Minimax Inequalities and Applications to Economies and Variational Inequalities
The Study of Minimax Inequalities and Applications to Economies and Variational Inequalities

Author: George Xian-Zhi Yuan

Publisher: American Mathematical Soc.

Published: 1998

Total Pages: 157

ISBN-13: 0821807471

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This book provides a unified treatment for the study of the existence of equilibria of abstract economics in topological vector spaces from the viewpoint of Ky Fan minimax inequalities, which strongly depend on his infinite dimensional version of the classical Knaster, Kuratowski and Mazurkiewicz Lemma (KKM Lemma) in 1961. Studied are applications of general system versions of minimax inequalities and generalized quasi-variational inequalities, and random abstract economies and its applications to the system of random quasi-variational inequalities are given.

Maximality Properties in Numerical Semigroups and Applications to One-Dimensional Analytically Irreducible Local Domains
Maximality Properties in Numerical Semigroups and Applications to One-Dimensional Analytically Irreducible Local Domains

Author: Valentina Barucci

Publisher: American Mathematical Soc.

Published: 1997

Total Pages: 95

ISBN-13: 0821805444

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In Chapter I, various (numerical) semigroup-theoretic concepts and constructions are introduced and characterized. Applications in Chapter II are made to the study of Noetherian local one-dimensional analytically irreducible integral domains, especially for the Gorenstein, maximal embedding dimension, and Arf cases, as well as to the so-called Kunz case, a pervasive kind of domain of Cohen-Macaulay type 2.

Symmetry Breaking for Compact Lie Groups
Symmetry Breaking for Compact Lie Groups

Author: Mike Field

Publisher: American Mathematical Soc.

Published: 1996

Total Pages: 185

ISBN-13: 0821804359

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This work comprises a general study of symmetry breaking for compact Lie groups in the context of equivariant bifurcation theory. We begin by extending the theory developed by Field and Richardson for absolutely irreducible representations of finite groups to general irreducible representations of compact Lie groups, while allowing for branches of relative equilibria and phenomena such as the Hopf bifurcation. We also present a general theory of determinacy for irreducible Lie group actions. We show that branching patterns for generic equivariant bifurcation problems defined on irreducible representations persist under perturbations by sufficiently high order non-equivariant terms.