This book grew out of a graduate course on 3-manifolds and is intended for a mathematically experienced audience that is new to low-dimensional topology. The exposition begins with the definition of a manifold, explores possible additional structures on manifolds, discusses the classification of surfaces, introduces key foundational results for 3-manifolds, and provides an overview of knot theory.
It then continues with more specialized topics by briefly considering triangulations of 3-manifolds, normal surface theory, and Heegaard splittings. The book finishes with a discussion of topics relevant to viewing 3-manifolds via the curve complex. With about figures and more than exercises, this book can serve as an excellent overview and starting point for the study of 3-manifolds. A new edition of a classic book originally published in and now updated and expanded to include the very latest developments.
The volume remains the single most important book on the topic. Features an attractive cover. This volume contains selected papers authored by speakers and participants of the Arbeitstagung, held at the Max Planck Institute for Mathematics in Bonn, Germany, from May The meeting and this resulting proceedings was dedicated to the memory of Friedrich Hirzebruch, who passed away on May 27, Hirzebruch organized the first Arbeitstagung in with a unique concept that would become its most distinctive feature: the program was not determined beforehand by the organizers, but during the meeting by all participants in an open discussion.
This ensured that the talks would be on the latest developments in mathematics and that many important results were presented at the conference for the first time. Written by leading mathematicians, the papers in this volume cover various topics from algebraic geometry, topology, analysis, operator theory, and representation theory and display the breadth and depth of pure mathematics that has always been characteristic of the Arbeitstagung. It facilitates new collaborations and mathematical advances through intensive residential research programs, each weeks in duration.
The peer-reviewed articles present original results or reviews on a topic related to the MATRIX program; the remaining contributions are predominantly lecture notes or short articles based on talks or activities at MATRIX. In particular, the smooth cobordism cup-product is defined from scratch and used as the main tool in a variety of settings.
Cobordism intersection forms are used to classify compact surfaces; their quadratic enhancements are developed and applied to studying the homotopy groups of spheres, the bordism group of immersed surfaces in a 3-manifold, and congruences mod 16 for the signature of intersection forms of 4-manifolds.
Nash manifolds and Nash's questions on the existence of real algebraic models are also discussed. This book will be useful as a textbook for beginning masters and doctoral students interested in differential topology, who have finished a standard undergraduate mathematics curriculum. It emphasizes an active learning approach, and exercises are included within the text as part of the flow of ideas. Experienced readers may use this book as a source of alternative, constructive approaches to results commonly presented in more advanced contexts with specialized techniques.
This book represents a novel approach to differential topology. Its main focus is to give a comprehensive introduction to the classification of manifolds, with special attention paid to the case of surfaces, for which the book provides a complete classification from many points of view: topological, smooth, constant curvature, complex, and conformal.
Each chapter briefly revisits basic results usually known to graduate students from an alternative perspective, focusing on surfaces. We provide full proofs of some remarkable results that sometimes are missed in basic courses e. Many examples and remarks are scattered through the book. Each chapter ends with an exhaustive collection of problems and a list of topics for further study. The book is primarily addressed to graduate students who did take standard introductory courses on algebraic topology, differential and Riemannian geometry, or algebraic geometry, but have not seen their deep interconnections, which permeate a modern approach to geometry and topology of manifolds.
Nigel Hitchin is one of the world's foremost figures in the fields of differential and algebraic geometry and their relations with mathematical physics, and he has been Savilian Professor of Geometry at Oxford since Geometry and Physics: A Festschrift in honour of Nigel Hitchin contain the proceedings of the conferences held in September in Aarhus, Oxford, and Madrid to mark Nigel Hitchin's 70th birthday, and to honour his far-reaching contributions to geometry and mathematical physics.
These texts contain 29 articles by contributors to the conference and other distinguished mathematicians working in related areas, including three Fields Medallists. The articles cover a broad range of topics in differential, algebraic and symplectic geometry, and also in mathematical physics. These volumes will be of interest to researchers and graduate students in geometry and mathematical physics.
As many readers will know, the 20th century was a time when the fields of mathematics and the sciences were seen as two separate entities. One sub-discipline that played a part in the union of the two subjects is Theoretical Physics. Breaking it down further came the fundamental theories, Relativity and Quantum theory, and later on Yang-Mills theory.
Advanced search. Author s Product display : Alexandru Scorpan. Abstract: This is a panorama of the topology of simply connected smooth manifolds of dimension four. Publication Month and Year: Copyright Year: Page Count: Cover Type: Softcover. Print ISBN Online ISBN Online ISSN:. Primary MSC: Secondary MSC: 14 ; Applied Math? MAA Book? Inquiry Based Learning? Electronic Media? Apparel or Gift: false. Online Price 1 Label: List. Online Price 1: View 1 excerpt, cites methods.
Four-manifolds with shadow-complexity one. We study the set of all closed oriented smooth 4-manifolds experimentally, according to a suitable complexity defined using Turaev shadows. This complexity roughly measures how complicated the … Expand.
In this paper, we give infinite families of counterexamples to two conjectures proposed by T. Lawson in his excellent review paper on the minimal genus problem [12]. Conjecture A: The … Expand. Multisections of Lefschetz fibrations and topology of symplectic 4—manifolds.
We initiate a study of positive multisections of Lefschetz fibrations via positive factorizations in framed mapping class groups of surfaces. Using our methods, one can effectively capture various … Expand. In this paper we are dealing with mean curvature flow with surgeries of two-convex hypersurfaces. Finite Group Actions on 4-Manifolds.
Suppose a finite, cyclic group G acts on a 4-manifold. What can we say about the fixed set of this action? In this talk, I will discuss some conditions one can impose on the action e.
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