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Author : Nikolai Saveliev
Publisher : Walter de Gruyter
ISBN 13 : 3110806355
Total Pages : 212 pages
Book Rating : 4.59/5 ( download)
Download or read book Lectures on the Topology of 3-Manifolds written by Nikolai Saveliev and published by Walter de Gruyter. This book was released on 2012-10-25 with total page 212 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Nikolai Saveliev
Publisher : Walter de Gruyter
ISBN 13 : 3110250365
Total Pages : 220 pages
Book Rating : 4.67/5 ( download)
Download or read book Lectures on the Topology of 3-Manifolds written by Nikolai Saveliev and published by Walter de Gruyter. This book was released on 2011-12-23 with total page 220 pages. Available in PDF, EPUB and Kindle. Book excerpt: Progress in low-dimensional topology has been very quick in the last three decades, leading to the solutions of many difficult problems. Among the earlier highlights of this period was Casson's λ-invariant that was instrumental in proving the vanishing of the Rohlin invariant of homotopy 3-spheres. The proof of the three-dimensional Poincaré conjecture has rendered this application moot but hardly made Casson's contribution less relevant: in fact, a lot of modern day topology, including a multitude of Floer homology theories, can be traced back to his λ-invariant. The principal goal of this book, now in its second revised edition, remains providing an introduction to the low-dimensional topology and Casson's theory; it also reaches out, when appropriate, to more recent research topics. The book covers some classical material, such as Heegaard splittings, Dehn surgery, and invariants of knots and links. It then proceeds through the Kirby calculus and Rohlin's theorem to Casson's invariant and its applications, and concludes with a brief overview of recent developments. The book will be accessible to graduate students in mathematics and theoretical physics familiar with some elementary algebraic and differential topology, including the fundamental group, basic homology theory, transversality, and Poincaré duality on manifolds.
Author : William H. Jaco
Publisher : American Mathematical Soc.
ISBN 13 : 0821816934
Total Pages : 266 pages
Book Rating : 4.36/5 ( download)
Download or read book Lectures on Three-Manifold Topology written by William H. Jaco and published by American Mathematical Soc.. This book was released on 1980-12-31 with total page 266 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 P. Thurston
Publisher :
ISBN 13 :
Total Pages : 502 pages
Book Rating : 4.49/5 ( download)
Download or read book The Geometry and Topology of Three-manifolds written by William P. Thurston and published by . This book was released on 1980 with total page 502 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Albrecht Dold
Publisher : Springer Science & Business Media
ISBN 13 : 3662007568
Total Pages : 389 pages
Book Rating : 4.63/5 ( download)
Download or read book Lectures on Algebraic Topology written by Albrecht Dold and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 389 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is essentially a book on singular homology and cohomology with special emphasis on products and manifolds. It does not treat homotopy theory except for some basic notions, some examples, and some applica tions of (co-)homology to homotopy. Nor does it deal with general(-ised) homology, but many formulations and arguments on singular homology are so chosen that they also apply to general homology. Because of these absences I have also omitted spectral sequences, their main applications in topology being to homotopy and general (co-)homology theory. Cech cohomology is treated in a simple ad hoc fashion for locally compact subsets of manifolds; a short systematic treatment for arbitrary spaces, emphasizing the universal property of the Cech-procedure, is contained in an appendix. The book grew out of a one-year's course on algebraic topology, and it can serve as a text for such a course. For a shorter basic course, say of half a year, one might use chapters II, III, IV (§§ 1-4), V (§§ 1-5, 7, 8), VI (§§ 3, 7, 9, 11, 12). As prerequisites the student should know the elementary parts of general topology, abelian group theory, and the language of categories - although our chapter I provides a little help with the latter two. For pedagogical reasons, I have treated integral homology only up to chapter VI; if a reader or teacher prefers to have general coefficients from the beginning he needs to make only minor adaptions.
Author : Jennifer Schultens
Publisher : American Mathematical Soc.
ISBN 13 : 1470410206
Total Pages : 298 pages
Book Rating : 4.09/5 ( download)
Download or read book Introduction to 3-Manifolds written by Jennifer Schultens and published by American Mathematical Soc.. This book was released on 2014-05-21 with total page 298 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 250 figures and more than 200 exercises, this book can serve as an excellent overview and starting point for the study of 3-manifolds.
Author : Danny Calegari
Publisher : Oxford University Press on Demand
ISBN 13 : 0198570082
Total Pages : 378 pages
Book Rating : 4.80/5 ( download)
Download or read book Foliations and the Geometry of 3-Manifolds written by Danny Calegari and published by Oxford University Press on Demand. This book was released on 2007-05-17 with total page 378 pages. Available in PDF, EPUB and Kindle. Book excerpt: This unique reference, aimed at research topologists, gives an exposition of the 'pseudo-Anosov' theory of foliations of 3-manifolds. This theory generalizes Thurston's theory of surface automorphisms and reveals an intimate connection between dynamics, geometry and topology in 3 dimensions. Significant themes returned to throughout the text include the importance of geometry, especially the hyperbolic geometry of surfaces, the importance of monotonicity, especially in1-dimensional and co-dimensional dynamics, and combinatorial approximation, using finite combinatorical objects such as train-tracks, branched surfaces and hierarchies to carry more complicated continuous objects.
Author : Chris Wendl
Publisher : Cambridge University Press
ISBN 13 : 1108759580
Total Pages : 198 pages
Book Rating : 4.88/5 ( download)
Download or read book Lectures on Contact 3-Manifolds, Holomorphic Curves and Intersection Theory written by Chris Wendl and published by Cambridge University Press. This book was released on 2020-03-26 with total page 198 pages. Available in PDF, EPUB and Kindle. Book excerpt: Intersection theory has played a prominent role in the study of closed symplectic 4-manifolds since Gromov's famous 1985 paper on pseudoholomorphic curves, leading to myriad beautiful rigidity results that are either inaccessible or not true in higher dimensions. Siefring's recent extension of the theory to punctured holomorphic curves allowed similarly important results for contact 3-manifolds and their symplectic fillings. Based on a series of lectures for graduate students in topology, this book begins with an overview of the closed case, and then proceeds to explain the essentials of Siefring's intersection theory and how to use it, and gives some sample applications in low-dimensional symplectic and contact topology. The appendices provide valuable information for researchers, including a concise reference guide on Siefring's theory and a self-contained proof of a weak version of the Micallef–White theorem.
Author : William Jaco
Publisher :
ISBN 13 :
Total Pages : 251 pages
Book Rating : 4.56/5 ( download)
Download or read book Lectures on Three-manifold Topology written by William Jaco and published by . This book was released on 1977 with total page 251 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Thomas Farrell
Publisher :
ISBN 13 : 9781571462879
Total Pages : 128 pages
Book Rating : 4.72/5 ( download)
Download or read book Introductory Lectures on Manifold Topology written by Thomas Farrell and published by . This book was released on 2014-04-25 with total page 128 pages. Available in PDF, EPUB and Kindle. Book excerpt: Since the 1950s, many new ideas and tools from algebra, and algebraic and geometric topology, have been applied to study the structure of high-dimensional differential and topological manifolds, and so today it can be difficult for beginners to delve through the literature. This volume is a helpful guide to the basic concepts and results of topology of manifolds -- including the h- and s-cobordism theorems, topological invariance of rational Pontryagin classes, surgery theory, and algebraic K-theory
