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Author: James Andrew Fowler Publisher: ISBN: 9781109208740 Category : Duality theory (Mathematics) Languages : en Pages : 120
Book Description
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: James Andrew Fowler Publisher: ISBN: 9781109208740 Category : Duality theory (Mathematics) Languages : en Pages : 120
Book Description
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
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: Jonathan Hillman Publisher: ISBN: 9781935107057 Category : Languages : en Pages :
Book Description
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: Adam Marsh Publisher: World Scientific ISBN: 9813233931 Category : Science Languages : en Pages : 301
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: Christopher Michael Duran Publisher: ISBN: Category : Poincaré series Languages : en Pages : 92
Book Description
This project is an expository study of the Poincaré duality theorem. Homology, cohomology groups of manifolds and other aglebraic and topological preliminaires are discussed.
Author: Andrew Ranicki Publisher: Cambridge University Press ISBN: 9780521420242 Category : Mathematics Languages : en Pages : 372
Book Description
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: James Andrew Fowler
Author: James Andrew Fowler
Author: Frank Albert Raymond
Author: Alejandro Adem
Author: Jonathan Hillman
Author: FRANK ALBERT RAYMOND
Author: Adam Marsh
Author: Christopher Michael Duran
Author: John Scott Downing
Author: Andrew Ranicki
Author: Nikolai Saveliev