Symmetric Automorphisms Of Free Products
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| Author | : Darryl McCullough |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 113 |
| Release | : 1996 |
| Genre | : Mathematics |
| ISBN | : 0821804596 |
The authors construct a complex [italic capital]K([italic capital]G) on which the automorphism group of [italic capital]G acts and use it to derive finiteness consequences for the group [capital Greek]Sigma [italic]Aut([italic capital]G). They prove that each component of [italic capital]K([italic capital]G) is contractible and describe the vertex stabilizers as elementary constructs involving the groups [italic capital]G[subscript italic]i and [italic]Aut([italic capital]G[subscript italic]i).
| Author | : Valentina Barucci |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 95 |
| Release | : 1997 |
| Genre | : Mathematics |
| ISBN | : 0821805444 |
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.
| Author | : Ambar Sengupta |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 98 |
| Release | : 1997 |
| Genre | : Mathematics |
| ISBN | : 0821804847 |
In this paper we develop a concrete description of connections on principal bundles, possibly non-trivial, over compact surfaces and use this description to construct the Yang-Mills measure which underlies the Euclidean quantum theory of gauge fields, involving compact gauge groups, on compact connected two-dimensional Riemannian manifolds (possibly with boundary). Using this measure we compute expectation values of important random variables, the Wilson loops variables, corresponding to a broad class of configurations of loops on the surface.
| Author | : Jack E. Graver |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 89 |
| Release | : 1997 |
| Genre | : Mathematics |
| ISBN | : 0821805568 |
The nine finite, planar, 3-connected, edge-transitive graphs have been known and studied for many centuries. The infinite, locally finite, planar, 3-connected, edge-transitive graphs can be classified according to the number of their end. The 1-ended graphs in this class were identified by Grünbaum and Shephard; Watkins characterized the 2-ended members. Any remaining graphs in this class must have uncountably may ends. In this work, infinite-ended members of this class are shown to exist. A more detailed classification scheme in terms of the types of Petrie walks in the graphs in this class and the local structure of their automorphism groups is presented.
| Author | : Eldar Straume |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 90 |
| Release | : 1997 |
| Genre | : Mathematics |
| ISBN | : 0821804839 |
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.
| Author | : Christopher Keil McCord |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 106 |
| Release | : 1998 |
| Genre | : Mathematics |
| ISBN | : 0821806920 |
The phase space of the spatial three-body problem is an open subset in R18. Holding the ten classical integrals of energu, center of mass, linear and angular momentum fixed defines an eight dimensional manifold. For fixed nonzero angular momentum, the topology of this manifold depends only on the energy. This volume computes the homology of this manifold for all energy values. This table of homology shows that for negative energy, the integral manifolds undergo seven bifurcations. Four of these are the well-known bifurcations due to central configurations, and three are due to "critical points at infinity". This disproves Birkhoffs conjecture that the bifurcations occur only at central configurations.
| Author | : Richard Bucher Sowers |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 145 |
| Release | : 1998 |
| Genre | : Mathematics |
| ISBN | : 0821806491 |
This volume studies the behaviour of a random heat kernel associated with a stochastic partial differential equation, and gives short-time expansion of this heat kernel. The author finds that the dominant exponential term is classical and depends only on the Riemannian distance function. The second exponential term is a work term and also has classical meaning. There is also a third non-negligible exponential term which blows up. The author finds an expression for this third exponential term which involves a random translation of the index form and the equations of Jacobi fields. In the process, he develops a method to approximate the heat kernel to any arbitrary degree of precision.
| Author | : Luigi Fontana |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 114 |
| Release | : 1998 |
| Genre | : Mathematics |
| ISBN | : 0821808303 |
In this book, the authors treat the full Hodge theory for the de Rham complex when calculated in the Sobolev topology rather than in the $L2$ topology. The use of the Sobolev topology strikingly alters the problem from the classical setup and gives rise to a new class of elliptic boundary value problems. The study takes place on both the upper half space and on a smoothly bounded domain. It features: a good introduction to elliptic theory, pseudo-differential operators, and boundary value problems; theorems completely explained and proved; and new geometric tools for differential analysis on domains and manifolds.
| Author | : Ajit Iqbal Singh |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 87 |
| Release | : 1996 |
| Genre | : Mathematics |
| ISBN | : 0821805398 |
It is now well know that the measure algebra [script capital]M([italic capital]G) of a locally compact group can be regarded as a subalgebra of the operator algebra [italic capital]B([italic capital]B([italic capital]L2([italic capital]G))) of the operator algebra [italic capital]B([italic capital]L2([italic capital]G)) of the Hilbert space [italic capital]L2([italic capital]G). We study the situation in hypergroups and find that, in general, the analogous map for them is neither an isometry nor a homomorphism. However, it is completely positive and completely bounded in certain ways. This work presents the related general theory and special examples.
| Author | : Serguei Germanovich Bobkov |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 127 |
| Release | : 1997 |
| Genre | : Art |
| ISBN | : 0821806424 |
For Borel probability measures on metric spaces, this text studies the interplay between isoperimetric and Sobolev-type inequalities. In particular the question of finding optimal constants via isoperimetric quantities is explored. Also given are necessary and sufficient conditions for the equivalence between the extremality of some sets in the isoperimetric problem and the validity of some analytic inequalities. The book devotes much attention to: the probability distributions on the real line; the normalized Lebesgue measure on the Euclidean sheres; and the canonical Gaussian measure on the Euclidean space.
