Topological Invariants of Stratified Spaces

Author: Markus Banagl
Publisher: Springer Science & Business Media
ISBN: 3540385878
Format: PDF, ePub
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The central theme of this book is the restoration of Poincaré duality on stratified singular spaces by using Verdier-self-dual sheaves such as the prototypical intersection chain sheaf on a complex variety. Highlights include complete and detailed proofs of decomposition theorems for self-dual sheaves, explanation of methods for computing twisted characteristic classes and an introduction to the author's theory of non-Witt spaces and Lagrangian structures.

Topology of Stratified Spaces

Author: Greg Friedman
Publisher: Cambridge University Press
ISBN: 052119167X
Format: PDF
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This book explores the study of singular spaces using techniques from areas within geometry and topology and the interactions among them.

Intersection Spaces Spatial Homology Truncation and String Theory

Author: Markus Banagl
Publisher: Springer Science & Business Media
ISBN: 3642125883
Format: PDF, Docs
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The present monograph introduces a method that assigns to certain classes of stratified spaces cell complexes, called intersection spaces, whose ordinary rational homology satisfies generalized Poincaré duality.

Singularities I

Author: Dũng Tráng Lê
Publisher: American Mathematical Soc.
ISBN: 082184458X
Format: PDF, ePub, Mobi
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This is the first part of the Proceedings of the meeting 'School and Workshop on the Geometry and Topology of Singularities', held in Cuernavaca, Mexico, from January 8th to 26th of 2007, in celebration of the 60th Birthday of Le Dung Trang.This volume contains fourteen cutting-edge research articles on algebraic and analytic aspects of singularities of spaces and maps. By reading this volume, and the accompanying volume on geometric and topological aspects of singularities, the reader should gain an appreciation for the depth, breadth, and beauty of the subject, and also find a rich source of questions and problems for future study.

Stratified Lie Groups and Potential Theory for Their Sub Laplacians

Author: Andrea Bonfiglioli
Publisher: Springer Science & Business Media
ISBN: 3540718974
Format: PDF, ePub, Mobi
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This book provides an extensive treatment of Potential Theory for sub-Laplacians on stratified Lie groups. It also provides a largely self-contained presentation of stratified Lie groups, and of their Lie algebra of left-invariant vector fields. The presentation is accessible to graduate students and requires no specialized knowledge in algebra or differential geometry.

The Topological Classification of Stratified Spaces

Author: Shmuel Weinberger
Publisher: University of Chicago Press
ISBN: 9780226885667
Format: PDF, ePub
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This book provides the theory for stratified spaces, along with important examples and applications, that is analogous to the surgery theory for manifolds. In the first expository account of this field, Weinberger provides topologists with a new way of looking at the classification theory of singular spaces with his original results. Divided into three parts, the book begins with an overview of modern high-dimensional manifold theory. Rather than including complete proofs of all theorems, Weinberger demonstrates key constructions, gives convenient formulations, and shows the usefulness of the technology. Part II offers the parallel theory for stratified spaces. Here, the topological category is most completely developed using the methods of "controlled topology." Many examples illustrating the topological invariance and noninvariance of obstructions and characteristic classes are provided. Applications for embeddings and immersions of manifolds, for the geometry of group actions, for algebraic varieties, and for rigidity theorems are found in Part III. This volume will be of interest to topologists, as well as mathematicians in other fields such as differential geometry, operator theory, and algebraic geometry.

Sheaves in Topology

Author: Alexandru Dimca
Publisher: Springer Science & Business Media
ISBN: 3642188680
Format: PDF, Mobi
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Constructible and perverse sheaves are the algebraic counterpart of the decomposition of a singular space into smooth manifolds. This introduction to the subject can be regarded as a textbook on modern algebraic topology, treating the cohomology of spaces with sheaf (as opposed to constant) coefficients. The author helps readers progress quickly from the basic theory to current research questions, thoroughly supported along the way by examples and exercises.