Spectral Asymptotics On Degenerating Hyperbolic 3 Manifolds
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Spectral Asymptotics On Degenerating Hyperbolic 3 Manifolds
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Author : Józef Dodziuk
language : en
Publisher: American Mathematical Soc.
Release Date : 1998
Spectral Asymptotics On Degenerating Hyperbolic 3 Manifolds written by Józef Dodziuk and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998 with Mathematics categories.
In this volume, the authors study asymptotics of the geometry and spectral theory of degenerating sequences of finite volume hyperbolic manifolds of three dimensions. Thurston's hyperbolic surgery theorem assets the existence of non-trivial sequences of finite volume hyperbolic three manifolds which converge to a three manifold with additional cusps. In the geometric aspect of their study, the authors use the convergence of hyperbolic metrics on the thick parts of the manifolds under consideration to investigate convergentce of tubes in the manifolds of the sequence to cusps of the limiting manifold. In the specral theory aspect of the work, they prove convergence of heat kernels. They then define a regualrized heat race associated to any finite volume, complete, hyperbolic three manifold, and study its asymptotic behaviour through degeneration. As an application of the analysis of the regularized heat trace, they study asymptotic behaviours of the spectral zeta function, determinant of the Laplacian, Selberg zeta function, and spectral counting functions through degeneration. The authors' methods are an adaptation to three dimensions of the earlier work of Jorgenson and Lundelius who investigated the asymptotic behaviour of spectral functions on degenerating families of finite area hyperbolic Riemann surfaces.
Periodic Hamiltonian Flows On Four Dimensional Manifolds
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Author : Yael Karshon
language : en
Publisher: American Mathematical Soc.
Release Date : 1999
Periodic Hamiltonian Flows On Four Dimensional Manifolds written by Yael Karshon and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999 with Mathematics categories.
This book is intended for graduate students and research mathematicians interested in global analysis, analysis on manifolds, and symplectic geometry.
The Defect Relation Of Meromorphic Maps On Parabolic Manifolds
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Author : George Lawrence Ashline
language : en
Publisher: American Mathematical Soc.
Release Date : 1999
The Defect Relation Of Meromorphic Maps On Parabolic Manifolds written by George Lawrence Ashline and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999 with Mathematics categories.
This book is intended for graduate students and research mathematicians working in several complex variables and analytic spaces.
A New Construction Of Homogeneous Quaternionic Manifolds And Related Geometric Structures
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Author : Vicente Cortés
language : en
Publisher: American Mathematical Soc.
Release Date : 2000
A New Construction Of Homogeneous Quaternionic Manifolds And Related Geometric Structures written by Vicente Cortés and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000 with Mathematics categories.
Let $V = {\mathbb R}^{p,q}$ be the pseudo-Euclidean vector space of signature $(p,q)$, $p\ge 3$ and $W$ a module over the even Clifford algebra $C\! \ell^0 (V)$. A homogeneous quaternionic manifold $(M,Q)$ is constructed for any $\mathfrak{spin}(V)$-equivariant linear map $\Pi : \wedge^2 W \rightarrow V$. If the skew symmetric vector valued bilinear form $\Pi$ is nondegenerate then $(M,Q)$ is endowed with a canonical pseudo-Riemannian metric $g$ such that $(M,Q,g)$ is a homogeneous quaternionic pseudo-Kahler manifold. If the metric $g$ is positive definite, i.e. a Riemannian metric, then the quaternionic Kahler manifold $(M,Q,g)$ is shown to admit a simply transitive solvable group of automorphisms. In this special case ($p=3$) we recover all the known homogeneous quaternionic Kahler manifolds of negative scalar curvature (Alekseevsky spaces) in a unified and direct way. If $p>3$ then $M$ does not admit any transitive action of a solvable Lie group and we obtain new families of quaternionic pseudo-Kahler manifolds. Then it is shown that for $q = 0$ the noncompact quaternionic manifold $(M,Q)$ can be endowed with a Riemannian metric $h$ such that $(M,Q,h)$ is a homogeneous quaternionic Hermitian manifold, which does not admit any transitive solvable group of isometries if $p>3$. The twistor bundle $Z \rightarrow M$ and the canonical ${\mathrm SO}(3)$-principal bundle $S \rightarrow M$ associated to the quaternionic manifold $(M,Q)$ are shown to be homogeneous under the automorphism group of the base. More specifically, the twistor space is a homogeneous complex manifold carrying an invariant holomorphic distribution $\mathcal D$ of complex codimension one, which is a complex contact structure if and only if $\Pi$ is nondegenerate. Moreover, an equivariant open holomorphic immersion $Z \rightarrow \bar{Z}$ into a homogeneous complex manifold $\bar{Z}$ of complex algebraic group is constructed. Finally, the construction is shown to have a natural mirror in the category of supermanifolds. In fact, for any $\mathfrak{spin}(V)$-equivariant linear map $\Pi : \vee^2 W \rightarrow V$ a homogeneous quaternionic supermanifold $(M,Q)$ is constructed and, moreover, a homogeneous quaternionic pseudo-Kahler supermanifold $(M,Q,g)$ if the symmetric vector valued bilinear form $\Pi$ is nondegenerate.
Existence And Persistence Of Invariant Manifolds For Semiflows In Banach Space
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Author : Peter W. Bates
language : en
Publisher: American Mathematical Soc.
Release Date : 1998
Existence And Persistence Of Invariant Manifolds For Semiflows In Banach Space written by Peter W. Bates and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998 with Mathematics categories.
Extends the theory for normally hyperbolic invariant manifolds to infinite dimensional dynamical systems in a Banach space, thereby providing tools for the study of PDE's and other infinite dimensional equations of evolution. In the process, the authors establish the existence of center-unstable and center-stable manifolds in a neighborhood of the unperturbed compact manifold. No index. Annotation copyrighted by Book News, Inc., Portland, OR
Homogeneous Integral Table Algebras Of Degree Three A Trilogy
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Author : Harvey I. Blau
language : en
Publisher: American Mathematical Soc.
Release Date : 2000
Homogeneous Integral Table Algebras Of Degree Three A Trilogy written by Harvey I. Blau and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000 with Mathematics categories.
Homogeneous integral table algebras of degree three with a faithful real element. The algebras of the title are classified to exact isomorphism; that is, the sets of structure constants which arise from the given basis are completely determined. Other results describe all possible extensions (pre-images), with a faithful element which is not necessarily real, of certain simple homogeneous integral table algebras of degree three. On antisymmetric homogeneous integral table algebras of degree three. This paper determines the homogeneous integral table algebras of degree three in which the given basis has a faithful element and has no nontrivial elements that are either real (symmetric) or linear, and where an additional hypothesis is satisfied. It is shown that all such bases must occur as the set of orbit sums in the complex group algebra of a finite abelian group under the action of a fixed-point-free automorphism oforder three. Homogeneous integral table algebras of degree three with no nontrivial linear elements. The algebras of the title which also have a faithful element are determined to exact isomorphism. All of the simple homogeneous integral table algebras of degree three are displayed, and the commutative association schemes in which all the nondiagonal relations have valency three and where some relation defines a connected graph on the underlying set are classified up to algebraic isomorphism.
Rational Homotopical Models And Uniqueness
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Author : Martin Majewski
language : en
Publisher: American Mathematical Soc.
Release Date : 2000
Rational Homotopical Models And Uniqueness written by Martin Majewski and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000 with Mathematics categories.
The main goal of this paper is to prove the following conjecture of Baues and Lemaire: the differential graded Lie Tlgebra associated with the Sullivan model of a space is homotopy equivalent to its Quillen model. In addition we show the same for the cellular Lie algebra model which we build from the simplicial analog of the classical Adams-Hilton model. It turns out that this cellular Lie algebra model is one link in a chain of models connecting the models of Quillen and Sullivan.The key result which makes all this possible is Anick's correspondence between differential graded Lie algebras and Hopf algebras up to homotopy. In addition we show that the Quillen model is a rational homotopical equivalence, and we conclude the same for the other models using our main result. Theconstruction of the three models is given in detail. The background from homotopy theory, differential algebra, and algebra is presented in great generality.
Categories Of Operator Modules Morita Equivalence And Projective Modules
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Author : David P. Blecher
language : en
Publisher: American Mathematical Soc.
Release Date : 2000
Categories Of Operator Modules Morita Equivalence And Projective Modules written by David P. Blecher and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000 with Mathematics categories.
We employ recent advances in the theory of operator spaces, also known as quantized functional analysis, to provide a context in which one can compare categories of modules over operator algebras that are not necessarily self-adjoint. We focus our attention on the category of Hilbert modules over an operator algebra and on the category of operator modules over an operator algebra. The module operations are assumed to be completely bounded - usually, completely contractive. Wedevelop the notion of a Morita context between two operator algebras A and B. This is a system (A,B,{} {A}X {B},{} {B} Y {A},(\cdot,\cdot),[\cdot,\cdot]) consisting of the algebras, two bimodules {A}X {B and {B}Y {A} and pairings (\cdot,\cdot) and [\cdot,\cdot] that induce (complete) isomorphisms betweenthe (balanced) Haagerup tensor products, X \otimes {hB} {} Y and Y \otimes {hA} {} X, and the algebras, A and B, respectively. Thus, formally, a Morita context is the same as that which appears in pure ring theory. The subtleties of the theory lie in the interplay between the pure algebra and the operator space geometry. Our analysis leads to viable notions of projective operator modules and dual operator modules. We show that two C*-algebras are Morita equivalent in our sense if and only ifthey are C*-algebraically strong Morita equivalent, and moreover the equivalence bimodules are the same. The distinctive features of the non-self-adjoint theory are illuminated through a number of examples drawn from complex analysis and the theory of incidence algebras over topological partial orders.Finally, an appendix provides links to the literature that developed since this Memoir was accepted for publication.
Hopf Algebras Polynomial Formal Groups And Raynaud Orders
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Author : Lindsay Childs
language : en
Publisher: American Mathematical Soc.
Release Date : 1998
Hopf Algebras Polynomial Formal Groups And Raynaud Orders written by Lindsay Childs and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998 with Mathematics categories.
This volume gives two new methods for constructing $p$-elementary Hopf algebra orders over the valuation ring $R$ of a local field $K$ containing the $p$-adic rational numbers. One method constructs Hopf orders using isogenies of commutative degree 2 polynomial formal groups of dimension $n$, and is built on a systematic study of such formal group laws. The other method uses an exponential generalization of a 1992 construction of Greither. Both constructions yield Raynaud orders as iterated extensions of rank $p$ Hopf algebras; the exponential method obtains all Raynaud orders whose invariants satisfy a certain $p$-adic condition.
Invariants Under Tori Of Rings Of Differential Operators And Related Topics
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Author : Ian Malcolm Musson
language : en
Publisher: American Mathematical Soc.
Release Date : 1998
Invariants Under Tori Of Rings Of Differential Operators And Related Topics written by Ian Malcolm Musson and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998 with Mathematics categories.
If $G$ is a reductive algebraic group acting rationally on a smooth affine variety $X$, then it is generally believed that $D(X) $ has properties very similar to those of enveloping algebras of semisimple Lie algebras. In this book, the authors show that this is indeed the case when $G$ is a torus and $X=k \times (k ) $. They give a precise description of the primitive ideals in $D(X) $ and study in detail the ring theoretical and homological properties of the minimal primitive quotients of $D(X) $. The latter are of the form $B =D(X) /({\germ g}-\chi({\germ g}))$ where ${\germ g}= {\rm Lie}(G)$, $\chi\in {\germ g} ast$ and ${\germ g}-\chi({\germ g})$ is the set of all $v-\chi(v)$ with $v\in {\germ g}$. They occur as rings of twisted differential operators on toric varieties. It is also proven that if $G$ is a torus acting rationally on a smooth affine variety, then $D(X/\!/G)$ is a simple ring.