High Dimensional Manifold Topology Proceedings Of The School
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Author |
: R. T. Farrell |
Publisher |
: World Scientific |
Total Pages |
: 516 |
Release |
: 2003 |
ISBN-10 |
: 9812704442 |
ISBN-13 |
: 9789812704443 |
Rating |
: 4/5 (42 Downloads) |
Synopsis High-dimensional Manifold Topology by : R. T. Farrell
This book covers topics such as manifolds with positive scalar curvature, pseudo-isotopy spectrum and controlled theory, and reduction of the Novikov and Borel conjectures for aspherical complexes to aspherical manifolds.
Author |
: F Thomas Farrell |
Publisher |
: World Scientific |
Total Pages |
: 510 |
Release |
: 2003-10-17 |
ISBN-10 |
: 9789814487078 |
ISBN-13 |
: 9814487074 |
Rating |
: 4/5 (78 Downloads) |
Synopsis High-dimensional Manifold Topology - Proceedings Of The School by : F Thomas Farrell
Contents: A Foliated Squeezing Theorem for Geometric Modules (A Bartels et al.)Equivariant Cellular Homology and Its Applications (B Chorny)Remarks on a Conjecture of Gromov and Lawson (W Dwyer et al.)Chain Complex Invariants for Group Actions (L E Jones)The Ore Condition, Affiliated Operators, and the Lamplighter Group (P A Linnell et al.)The Surgery Exact Sequence Revisited (E K Pedersen)K-theory for Proper Smooth Actions of Totally Disconnected Groups (J Sauer)Geometric Chain Homotopy Equivalences between Novikov Complexes (D Schütz)and other papers Readership: Graduate students and researchers in geometry and topology. Keywords:High-Dimensional Manifold Topology;Operator Algebras;K-Theory;L-Theory;Foliated Control Theory
Author |
: Abdus Salam International Centre for Theoretical Physics |
Publisher |
: World Scientific |
Total Pages |
: 510 |
Release |
: 2003 |
ISBN-10 |
: 9789812382238 |
ISBN-13 |
: 9812382232 |
Rating |
: 4/5 (38 Downloads) |
Synopsis High-dimensional Manifold Topology by : Abdus Salam International Centre for Theoretical Physics
Contents: A Foliated Squeezing Theorem for Geometric Modules (A Bartels et al.); Equivariant Cellular Homology and Its Applications (B Chorny); Remarks on a Conjecture of Gromov and Lawson (W Dwyer et al.); Chain Complex Invariants for Group Actions (L E Jones); The Ore Condition, Affiliated Operators, and the Lamplighter Group (P A Linnell et al.); The Surgery Exact Sequence Revisited (E K Pedersen); K-theory for Proper Smooth Actions of Totally Disconnected Groups (J Sauer); Geometric Chain Homotopy Equivalences between Novikov Complexes (D Schütz); and other papers;
Author |
: Alberto Cavicchioli |
Publisher |
: |
Total Pages |
: 146 |
Release |
: 2016 |
ISBN-10 |
: 3037191562 |
ISBN-13 |
: 9783037191569 |
Rating |
: 4/5 (62 Downloads) |
Synopsis Higher-dimensional Generalized Manifolds by : Alberto Cavicchioli
Generalized manifolds are a most fascinating subject to study. They were introduced in the 1930s, when topologists tried to detect topological manifolds among more general spaces. (This is now called the manifold recognition problem.) As such, generalized manifolds have served to enhance our understanding of the nature of genuine manifolds. However, it soon became more important to study the category of generalized manifolds itself. A breakthrough was made in the 1990s, when several topologists discovered a systematic way of constructing higher-dimensional generalized manifolds, based on advanced surgery techniques. In fact, the development of controlled surgery theory and the study of generalized manifolds developed in parallel. In this process, earlier studies of geometric surgery turned out to be very helpful. Generalized manifolds will continue to be an attractive subject to study, for there remain several unsolved fundamental problems. Moreover, they hold promise for new research, e.g. for finding appropriate structures on these spaces which could bring to light geometric (or even analytic) aspects of higher-dimensional generalized manifolds. This is the first book to systematically collect the most important material on higher-dimensional generalized manifolds and controlled surgery. It is self-contained and its extensive list of references reflects the historic development. The book is based on the authors' graduate courses and seminars, as well as their talks given at various meetings, and is suitable for advanced graduate students and researchers in algebraic and geometric topology.
Author |
: Katsuro Sakai |
Publisher |
: Springer Nature |
Total Pages |
: 619 |
Release |
: 2020-11-21 |
ISBN-10 |
: 9789811575754 |
ISBN-13 |
: 9811575754 |
Rating |
: 4/5 (54 Downloads) |
Synopsis Topology of Infinite-Dimensional Manifolds by : Katsuro Sakai
An infinite-dimensional manifold is a topological manifold modeled on some infinite-dimensional homogeneous space called a model space. In this book, the following spaces are considered model spaces: Hilbert space (or non-separable Hilbert spaces), the Hilbert cube, dense subspaces of Hilbert spaces being universal spaces for absolute Borel spaces, the direct limit of Euclidean spaces, and the direct limit of Hilbert cubes (which is homeomorphic to the dual of a separable infinite-dimensional Banach space with bounded weak-star topology). This book is designed for graduate students to acquire knowledge of fundamental results on infinite-dimensional manifolds and their characterizations. To read and understand this book, some background is required even for senior graduate students in topology, but that background knowledge is minimized and is listed in the first chapter so that references can easily be found. Almost all necessary background information is found in Geometric Aspects of General Topology, the author's first book. Many kinds of hyperspaces and function spaces are investigated in various branches of mathematics, which are mostly infinite-dimensional. Among them, many examples of infinite-dimensional manifolds have been found. For researchers studying such objects, this book will be very helpful. As outstanding applications of Hilbert cube manifolds, the book contains proofs of the topological invariance of Whitehead torsion and Borsuk’s conjecture on the homotopy type of compact ANRs. This is also the first book that presents combinatorial ∞-manifolds, the infinite-dimensional version of combinatorial n-manifolds, and proofs of two remarkable results, that is, any triangulation of each manifold modeled on the direct limit of Euclidean spaces is a combinatorial ∞-manifold and the Hauptvermutung for them is true.
Author |
: Vincenzo Ancona |
Publisher |
: Springer |
Total Pages |
: 309 |
Release |
: 2014-08-27 |
ISBN-10 |
: 9783319052540 |
ISBN-13 |
: 3319052543 |
Rating |
: 4/5 (40 Downloads) |
Synopsis Trends in Contemporary Mathematics by : Vincenzo Ancona
The topics faced in this book cover a large spectrum of current trends in mathematics, such as Shimura varieties and the Lang lands program, zonotopal combinatorics, non linear potential theory, variational methods in imaging, Riemann holonomy and algebraic geometry, mathematical problems arising in kinetic theory, Boltzmann systems, Pell's equations in polynomials, deformation theory in non commutative algebras. This work contains a selection of contributions written by international leading mathematicians who were speakers at the "INdAM Day", an initiative born in 2004 to present the most recent developments in contemporary mathematics.
Author |
: Francesco Masulli |
Publisher |
: World Scientific |
Total Pages |
: 417 |
Release |
: 1994-10-24 |
ISBN-10 |
: 9789814551533 |
ISBN-13 |
: 9814551538 |
Rating |
: 4/5 (33 Downloads) |
Synopsis Neural Networks In Biomedicine - Proceedings Of The Advanced School Of The Italian Bromedical Physics Association by : Francesco Masulli
Methods based on neural networks are assuming an increasing role in biomedical research. This book presents an introduction to the application of neural networks and related areas of artificial intelligence to biological structure analysis, biomedical images understanding, electrophysiologic signal analysis and other stimulating issues of biomedicine.This book, which will include the latest advances and developments in the field, will be of value to researchers in neural networks and biomedicine.
Author |
: Wolfgang Lück |
Publisher |
: Springer Nature |
Total Pages |
: 956 |
Release |
: 2024 |
ISBN-10 |
: 9783031563348 |
ISBN-13 |
: 3031563344 |
Rating |
: 4/5 (48 Downloads) |
Synopsis Surgery Theory by : Wolfgang Lück
This monograph provides a comprehensive introduction to surgery theory, the main tool in the classification of manifolds. Surgery theory was developed to carry out the so-called Surgery Program, a basic strategy to decide whether two closed manifolds are homeomorphic or diffeomorphic. This book provides a detailed explanation of all the ingredients necessary for carrying out the surgery program, as well as an in-depth discussion of the obstructions that arise. The components include the surgery step, the surgery obstruction groups, surgery obstructions, and the surgery exact sequence. This machinery is applied to homotopy spheres, the classification of certain fake spaces, and topological rigidity. The book also offers a detailed description of Ranicki's chain complex version, complete with a proof of its equivalence to the classical approach developed by Browder, Novikov, Sullivan, and Wall. This book has been written for learning surgery theory and includes numerous exercises. With full proofs and detailed explanations, it also provides an invaluable reference for working mathematicians. Each chapter has been designed to be largely self-contained and includes a guide to help readers navigate the material, making the book highly suitable for lecture courses, seminars, and reading courses.
Author |
: Wolfgang Lück |
Publisher |
: Springer Science & Business Media |
Total Pages |
: 604 |
Release |
: 2013-03-09 |
ISBN-10 |
: 9783662046876 |
ISBN-13 |
: 3662046873 |
Rating |
: 4/5 (76 Downloads) |
Synopsis L2-Invariants: Theory and Applications to Geometry and K-Theory by : Wolfgang Lück
In algebraic topology some classical invariants - such as Betti numbers and Reidemeister torsion - are defined for compact spaces and finite group actions. They can be generalized using von Neumann algebras and their traces, and applied also to non-compact spaces and infinite groups. These new L2-invariants contain very interesting and novel information and can be applied to problems arising in topology, K-Theory, differential geometry, non-commutative geometry and spectral theory. The book, written in an accessible manner, presents a comprehensive introduction to this area of research, as well as its most recent results and developments.
Author |
: Eric Friedlander |
Publisher |
: Springer Science & Business Media |
Total Pages |
: 1148 |
Release |
: 2005-07-18 |
ISBN-10 |
: 9783540230199 |
ISBN-13 |
: 354023019X |
Rating |
: 4/5 (99 Downloads) |
Synopsis Handbook of K-Theory by : Eric Friedlander
This handbook offers a compilation of techniques and results in K-theory. Each chapter is dedicated to a specific topic and is written by a leading expert. Many chapters present historical background; some present previously unpublished results, whereas some present the first expository account of a topic; many discuss future directions as well as open problems. It offers an exposition of our current state of knowledge as well as an implicit blueprint for future research.