Poincare Duality in Homology Manifolds PDF Download

Author: Frank Albert Raymond
Publisher:
ISBN:
Category : Homology theory
Languages : en
Pages : 164

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Author: James Andrew Fowler
Publisher:
ISBN: 9781109208740
Category : Duality theory (Mathematics)
Languages : en
Pages : 120

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However, we also show that this is rather exceptional: uniform lattices in semisimple Lie groups which contain p-torsion (for p ≠ 2) do not act freely on Q -acyclic Q -homology manifolds; obstructions include an equivariant finiteness obstruction and a lifting problem for rational controlled symmetric signatures.

Author: Alejandro Adem
Publisher: Cambridge University Press
ISBN: 1139464485
Category : Mathematics
Languages : en
Pages : 138

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Book Description
An introduction to the theory of orbifolds from a modern perspective, combining techniques from geometry, algebraic topology and algebraic geometry. One of the main motivations, and a major source of examples, is string theory, where orbifolds play an important role. The subject is first developed following the classical description analogous to manifold theory, after which the book branches out to include the useful description of orbifolds provided by groupoids, as well as many examples in the context of algebraic geometry. Classical invariants such as de Rham cohomology and bundle theory are developed, a careful study of orbifold morphisms is provided, and the topic of orbifold K-theory is covered. The heart of this book, however, is a detailed description of the Chen-Ruan cohomology, which introduces a product for orbifolds and has had significant impact. The final chapter includes explicit computations for a number of interesting examples.

Author: FRANK ALBERT RAYMOND
Publisher:
ISBN:
Category :
Languages : en
Pages : 164

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Author: Andrew Ranicki
Publisher: Cambridge University Press
ISBN: 9780521420242
Category : Mathematics
Languages : en
Pages : 372

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Assuming no previous acquaintance with surgery theory and justifying all the algebraic concepts used by their relevance to topology, Dr Ranicki explains the applications of quadratic forms to the classification of topological manifolds, in a unified algebraic framework.

Author: Jonathan Hillman
Publisher:
ISBN: 9781935107057
Category :
Languages : en
Pages :

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Poincaré duality is central to the understanding of manifold topology. Dimension 3 is critical in various respects, being between the known territory of surfaces and the wilderness manifest in dimensions >= 4. The main thrust of 3-manifold topology for the past half century has been to show that aspherical closed 3-manifolds are determined by their fundamental groups. Relatively little attention has been given to the question of which groups arise. This book is the first comprehensive account of what is known about PD3-complexes, which model the homotopy types of closed 3-manifolds, and PD3-groups, which correspond to aspherical 3-manifolds. In the first half we show that every P2-irreducible PD3-complex is a connected sum of indecomposables, which are either aspherical or have virtually free fundamental group, and largely determine the latter class. The picture is much less complete in the aspherical case. We sketch several possible approaches for tackling the central question, whether every PD3-group is a 3-manifold group, and then explore properties of subgroups of PD3-groups, unifying many results of 3-manifold topology. We conclude with an appendix listing over 60 questions. Our general approach is to prove most assertions which are specifically about Poincaré duality in dimension 3, but otherwise to cite standard references for the major supporting results.

Author: Markus Banagl
Publisher: Springer Science & Business Media
ISBN: 3540385878
Category : Mathematics
Languages : en
Pages : 266

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Book Description
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.

Author: Adam Marsh
Publisher: World Scientific
ISBN: 9813233931
Category : Science
Languages : en
Pages : 301

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Book Description
This unique book complements traditional textbooks by providing a visual yet rigorous survey of the mathematics used in theoretical physics beyond that typically covered in undergraduate math and physics courses. The exposition is pedagogical but compact, and the emphasis is on defining and visualizing concepts and relationships between them, as well as listing common confusions, alternative notations and jargon, and relevant facts and theorems. Special attention is given to detailed figures and geometric viewpoints. Certain topics which are well covered in textbooks, such as historical motivations, proofs and derivations, and tools for practical calculations, are avoided. The primary physical models targeted are general relativity, spinors, and gauge theories, with notable chapters on Riemannian geometry, Clifford algebras, and fiber bundles.

Author: Nikolai Saveliev
Publisher: Walter de Gruyter
ISBN: 9783110162721
Category : Mathematics
Languages : en
Pages : 220

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Author: Anatoly Fomenko
Publisher: Springer
ISBN: 3319234889
Category : Mathematics
Languages : en
Pages : 635

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Book Description
This textbook on algebraic topology updates a popular textbook from the golden era of the Moscow school of I. M. Gelfand. The first English translation, done many decades ago, remains very much in demand, although it has been long out-of-print and is difficult to obtain. Therefore, this updated English edition will be much welcomed by the mathematical community. Distinctive features of this book include: a concise but fully rigorous presentation, supplemented by a plethora of illustrations of a high technical and artistic caliber; a huge number of nontrivial examples and computations done in detail; a deeper and broader treatment of topics in comparison to most beginning books on algebraic topology; an extensive, and very concrete, treatment of the machinery of spectral sequences. The second edition contains an entirely new chapter on K-theory and the Riemann-Roch theorem (after Hirzebruch and Grothendieck).