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Author: William H. Jaco
Publisher: American Mathematical Soc.
ISBN: 0821816934
Category : Mathematics
Languages : en
Pages : 266
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Book Description
This manuscript is a detailed presentation of the ten lectures given by the author at the NSF Regional Conference on Three-Manifold Topology, held October 1977, at Virginia Polytechnic Institute and State University. The purpose of the conference was to present the current state of affairs in three-manifold topology and to integrate the classical results with the many recent advances and new directions.
Author: William H. Jaco
Publisher: American Mathematical Soc.
ISBN: 0821816934
Category : Mathematics
Languages : en
Pages : 266
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Book Description
This manuscript is a detailed presentation of the ten lectures given by the author at the NSF Regional Conference on Three-Manifold Topology, held October 1977, at Virginia Polytechnic Institute and State University. The purpose of the conference was to present the current state of affairs in three-manifold topology and to integrate the classical results with the many recent advances and new directions.
Author: Krzysztof Galicki
Publisher: Springer Science & Business Media
ISBN: 0817647430
Category : Mathematics
Languages : en
Pages : 303
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Book Description
Riemannian Topology and Structures on Manifolds results from a similarly entitled conference held on the occasion of Charles P. Boyer’s 65th birthday. The various contributions to this volume discuss recent advances in the areas of positive sectional curvature, Kähler and Sasakian geometry, and their interrelation to mathematical physics, especially M and superstring theory. Focusing on these fundamental ideas, this collection presents review articles, original results, and open problems of interest.
Author: A.A. Ranicki
Publisher: Springer Science & Business Media
ISBN: 9401733430
Category : Mathematics
Languages : en
Pages : 192
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Book Description
The Hauptvermutung is the conjecture that any two triangulations of a poly hedron are combinatorially equivalent. The conjecture was formulated at the turn of the century, and until its resolution was a central problem of topology. Initially, it was verified for low-dimensional polyhedra, and it might have been expected that furt her development of high-dimensional topology would lead to a verification in all dimensions. However, in 1961 Milnor constructed high-dimensional polyhedra with combinatorially inequivalent triangulations, disproving the Hauptvermutung in general. These polyhedra were not manifolds, leaving open the Hauptvermu tung for manifolds. The development of surgery theory led to the disproof of the high-dimensional manifold Hauptvermutung in the late 1960's. Unfortunately, the published record of the manifold Hauptvermutung has been incomplete, as was forcefully pointed out by Novikov in his lecture at the Browder 60th birthday conference held at Princeton in March 1994. This volume brings together the original 1967 papers of Casson and Sulli van, and the 1968/1972 'Princeton notes on the Hauptvermutung' of Armstrong, Rourke and Cooke, making this work physically accessible. These papers include several other results which have become part of the folklore but of which proofs have never been published. My own contribution is intended to serve as an intro duction to the Hauptvermutung, and also to give an account of some more recent developments in the area. In preparing the original papers for publication, only minimal changes of punctuation etc.
Author: Andrew Ranicki
Publisher: Oxford University Press
ISBN: 9780198509240
Category : Mathematics
Languages : en
Pages : 396
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Book Description
This book is an introduction to surgery theory: the standard classification method for high-dimensional manifolds. It is aimed at graduate students, who have already had a basic topology course, and would now like to understand the topology of high-dimensional manifolds. This text contains entry-level accounts of the various prerequisites of both algebra and topology, including basic homotopy and homology, Poincare duality, bundles, co-bordism, embeddings, immersions, Whitehead torsion, Poincare complexes, spherical fibrations and quadratic forms and formations. While concentrating on the basic mechanics of surgery, this book includes many worked examples, useful drawings for illustration of the algebra and references for further reading.
Author: William Browder
Publisher:
ISBN: 9780691027296
Category : Mathematics
Languages : en
Pages : 340
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Book Description
This collection brings together influential papers by mathematicians exploring the research frontiers of topology, one of the most important developments of modern mathematics. The papers cover a wide range of topological specialties, including tools for the analysis of group actions on manifolds, calculations of algebraic K-theory, a result on analytic structures on Lie group actions, a presentation of the significance of Dirac operators in smoothing theory, a discussion of the stable topology of 4-manifolds, an answer to the famous question about symmetries of simply connected manifolds, and a fresh perspective on the topological classification of linear transformations. The contributors include A. Adem, A. H. Assadi, M. Bökstedt, S. E. Cappell, R. Charney, M. W. Davis, P. J. Eccles, M. H. Freedman, I. Hambleton, J. C. Hausmann, S. Illman, G. Katz, M. Kreck, W. Lück, I. Madsen, R. J. Milgram, J. Morava, E. K. Pedersen, V. Puppe, F. Quinn, A. Ranicki, J. L. Shaneson, D. Sullivan, P. Teichner, Z. Wang, and S. Weinberger.
Author: J. P. May
Publisher: University of Chicago Press
ISBN: 9780226511832
Category : Mathematics
Languages : en
Pages : 262
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Book Description
Algebraic topology is a basic part of modern mathematics, and some knowledge of this area is indispensable for any advanced work relating to geometry, including topology itself, differential geometry, algebraic geometry, and Lie groups. This book provides a detailed treatment of algebraic topology both for teachers of the subject and for advanced graduate students in mathematics either specializing in this area or continuing on to other fields. J. Peter May's approach reflects the enormous internal developments within algebraic topology over the past several decades, most of which are largely unknown to mathematicians in other fields. But he also retains the classical presentations of various topics where appropriate. Most chapters end with problems that further explore and refine the concepts presented. The final four chapters provide sketches of substantial areas of algebraic topology that are normally omitted from introductory texts, and the book concludes with a list of suggested readings for those interested in delving further into the field.
Author:
Publisher:
ISBN:
Category : Union catalogs
Languages : en
Pages : 616
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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: Craig D. Hodgson
Publisher: American Mathematical Soc.
ISBN: 0821884808
Category : Mathematics
Languages : en
Pages : 395
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Book Description
This book contains the proceedings of the conference Geometry & Topology Down Under, held July 11-22, 2011, at the University of Melbourne, Parkville, Australia, in honour of Hyam Rubinstein. The main topic of the book is low-dimensional geometry and topology. It includes both survey articles based on courses presented at the conferences and research articles devoted to important questions in low-dimensional geometry. Together, these contributions show how methods from different fields of mathematics contribute to the study of 3-manifolds and Gromov hyperbolic groups. It also contains a list of favorite problems by Hyam Rubinstein.
Author: Matthew G. Brin
Publisher: American Mathematical Soc.
ISBN: 0821824740
Category : Homotopy theory
Languages : en
Pages : 86
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Book Description
This paper continues a series by the authors on non-compact 3-manifolds. We describe the structure, up to end homeomorphism, of those orientable, non-compact 3-manifolds in which all loops near infinity [symbol] homotop to infinity [symbol] while staying near infinity [symbol] (the proper homotopy condition "end 1-movability" of the title). This extends previous work by others and by the authors because end 1-movability is weaker than properties studied before, and also because our result is the first to analyse a class of non-compact 3-manifolds whose defining properties include neither irreducibilty nor compact boundary. Our main tool is the end reduction--introduced in our earlier papers, developed further. End reductions are "simple" approximations of a non-compact 3-manifold that capture many of the manifold's properties.
