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Author: Jesús A. Álvarez López
Publisher: Springer
ISBN: 3319941321
Category : Mathematics
Languages : en
Pages : 178
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Book Description
This book provides a detailed introduction to the coarse quasi-isometry of leaves of a foliated space and describes the cases where the generic leaves have the same quasi-isometric invariants. Every leaf of a compact foliated space has an induced coarse quasi-isometry type, represented by the coarse metric defined by the length of plaque chains given by any finite foliated atlas. When there are dense leaves either all dense leaves without holonomy are uniformly coarsely quasi-isometric to each other, or else every leaf is coarsely quasi-isometric to just meagerly many other leaves. Moreover, if all leaves are dense, the first alternative is characterized by a condition on the leaves called coarse quasi-symmetry. Similar results are proved for more specific coarse invariants, like growth type, asymptotic dimension, and amenability. The Higson corona of the leaves is also studied. All the results are richly illustrated with examples. The book is primarily aimed at researchers on foliated spaces. More generally, specialists in geometric analysis, topological dynamics, or metric geometry may also benefit from it.
Author: Jesús A. Álvarez López
Publisher: Springer
ISBN: 3319941321
Category : Mathematics
Languages : en
Pages : 178
Get Book Here
Book Description
This book provides a detailed introduction to the coarse quasi-isometry of leaves of a foliated space and describes the cases where the generic leaves have the same quasi-isometric invariants. Every leaf of a compact foliated space has an induced coarse quasi-isometry type, represented by the coarse metric defined by the length of plaque chains given by any finite foliated atlas. When there are dense leaves either all dense leaves without holonomy are uniformly coarsely quasi-isometric to each other, or else every leaf is coarsely quasi-isometric to just meagerly many other leaves. Moreover, if all leaves are dense, the first alternative is characterized by a condition on the leaves called coarse quasi-symmetry. Similar results are proved for more specific coarse invariants, like growth type, asymptotic dimension, and amenability. The Higson corona of the leaves is also studied. All the results are richly illustrated with examples. The book is primarily aimed at researchers on foliated spaces. More generally, specialists in geometric analysis, topological dynamics, or metric geometry may also benefit from it.
Author: Vladimir Rovenski
Publisher: Springer Nature
ISBN: 3031505867
Category :
Languages : en
Pages : 323
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Book Description
Author: Christian Rosendal
Publisher: Cambridge University Press
ISBN: 110884247X
Category : Mathematics
Languages : en
Pages : 309
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Book Description
Provides a general framework for doing geometric group theory for non-locally-compact topological groups arising in mathematical practice.
Author: American Mathematical Society
Publisher:
ISBN:
Category : Mathematics
Languages : en
Pages : 726
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Book Description
Author: Ana Cannas da Silva
Publisher: Springer
ISBN: 354045330X
Category : Mathematics
Languages : en
Pages : 240
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Book Description
The goal of these notes is to provide a fast introduction to symplectic geometry for graduate students with some knowledge of differential geometry, de Rham theory and classical Lie groups. This text addresses symplectomorphisms, local forms, contact manifolds, compatible almost complex structures, Kaehler manifolds, hamiltonian mechanics, moment maps, symplectic reduction and symplectic toric manifolds. It contains guided problems, called homework, designed to complement the exposition or extend the reader's understanding. There are by now excellent references on symplectic geometry, a subset of which is in the bibliography of this book. However, the most efficient introduction to a subject is often a short elementary treatment, and these notes attempt to serve that purpose. This text provides a taste of areas of current research and will prepare the reader to explore recent papers and extensive books on symplectic geometry where the pace is much faster. For this reprint numerous corrections and clarifications have been made, and the layout has been improved.
Author: Siegfried Bosch
Publisher: Springer
ISBN: 3319044176
Category : Mathematics
Languages : en
Pages : 255
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Book Description
The aim of this work is to offer a concise and self-contained 'lecture-style' introduction to the theory of classical rigid geometry established by John Tate, together with the formal algebraic geometry approach launched by Michel Raynaud. These Lectures are now viewed commonly as an ideal means of learning advanced rigid geometry, regardless of the reader's level of background. Despite its parsimonious style, the presentation illustrates a number of key facts even more extensively than any other previous work. This Lecture Notes Volume is a revised and slightly expanded version of a preprint that appeared in 2005 at the University of Münster's Collaborative Research Center "Geometrical Structures in Mathematics".
Author:
Publisher:
ISBN:
Category : Mathematics
Languages : en
Pages : 994
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Book Description
Author: Alain Connes
Publisher: Springer
ISBN: 3540397027
Category : Mathematics
Languages : en
Pages : 364
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Book Description
Noncommutative Geometry is one of the most deep and vital research subjects of present-day Mathematics. Its development, mainly due to Alain Connes, is providing an increasing number of applications and deeper insights for instance in Foliations, K-Theory, Index Theory, Number Theory but also in Quantum Physics of elementary particles. The purpose of the Summer School in Martina Franca was to offer a fresh invitation to the subject and closely related topics; the contributions in this volume include the four main lectures, cover advanced developments and are delivered by prominent specialists.
Author: Danny Calegari
Publisher: Oxford University Press on Demand
ISBN: 0198570082
Category : Mathematics
Languages : en
Pages : 378
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Book Description
This unique reference, aimed at research topologists, gives an exposition of the 'pseudo-Anosov' theory of foliations of 3-manifolds. This theory generalizes Thurston's theory of surface automorphisms and reveals an intimate connection between dynamics, geometry and topology in 3 dimensions. Significant themes returned to throughout the text include the importance of geometry, especially the hyperbolic geometry of surfaces, the importance of monotonicity, especially in1-dimensional and co-dimensional dynamics, and combinatorial approximation, using finite combinatorical objects such as train-tracks, branched surfaces and hierarchies to carry more complicated continuous objects.
Author: Daniel Huybrechts
Publisher: Cambridge University Press
ISBN: 1139485822
Category : Mathematics
Languages : en
Pages : 345
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Book Description
This edition has been updated to reflect recent advances in the theory of semistable coherent sheaves and their moduli spaces. The authors review changes in the field and point the reader towards further literature. An ideal text for graduate students or mathematicians with a background in algebraic geometry.
