Selected Applications of Geometry to Low-dimensional Topology PDF Download
Are you looking for read ebook online? Search for your book and save it on your Kindle device, PC, phones or tablets. Download Selected Applications of Geometry to Low-dimensional Topology PDF full book. Access full book title Selected Applications of Geometry to Low-dimensional Topology by Michael H. Freedman. Download full books in PDF and EPUB format.
Author: Michael H. Freedman
Publisher: American Mathematical Soc.
ISBN: 0821870009
Category : Mathematics
Languages : en
Pages : 79
Get Book
Book Description
The inaugural volume in the popular AMS softcover series designed to make more widely available some of the outstanding lectures presented by various faculty in North America.
Author: Michael H. Freedman
Publisher: American Mathematical Soc.
ISBN: 0821870009
Category : Mathematics
Languages : en
Pages : 79
Get Book
Book Description
The inaugural volume in the popular AMS softcover series designed to make more widely available some of the outstanding lectures presented by various faculty in North America.
Author: Vassily Olegovich Manturov
Publisher: World Scientific
ISBN: 9814630632
Category : Mathematics
Languages : en
Pages : 540
Get Book
Book Description
This book consists of a selection of articles devoted to new ideas and developments in low dimensional topology. Low dimensions refer to dimensions three and four for the topology of manifolds and their submanifolds. Thus we have papers related to both manifolds and to knotted submanifolds of dimension one in three (classical knot theory) and two in four (surfaces in four dimensional spaces). Some of the work involves virtual knot theory where the knots are abstractions of classical knots but can be represented by knots embedded in surfaces. This leads both to new interactions with classical topology and to new interactions with essential combinatorics.
Author: Tomasz Mrowka
Publisher: American Mathematical Soc.
ISBN: 0821886967
Category : Mathematics
Languages : en
Pages : 331
Get Book
Book Description
Low-dimensional topology has long been a fertile area for the interaction of many different disciplines of mathematics, including differential geometry, hyperbolic geometry, combinatorics, representation theory, global analysis, classical mechanics, and theoretical physics. The Park City Mathematics Institute summer school in 2006 explored in depth the most exciting recent aspects of this interaction, aimed at a broad audience of both graduate students and researchers. The present volume is based on lectures presented at the summer school on low-dimensional topology. These notes give fresh, concise, and high-level introductions to these developments, often with new arguments not found elsewhere. The volume will be of use both to graduate students seeking to enter the field of low-dimensional topology and to senior researchers wishing to keep up with current developments. The volume begins with notes based on a special lecture by John Milnor about the history of the topology of manifolds. It also contains notes from lectures by Cameron Gordon on the basics of three-manifold topology and surgery problems, Mikhail Khovanov on his homological invariants for knots, John Etnyre on contact geometry, Ron Fintushel and Ron Stern on constructions of exotic four-manifolds, David Gabai on the hyperbolic geometry and the ending lamination theorem, Zoltan Szabo on Heegaard Floer homology for knots and three manifolds, and John Morgan on Hamilton's and Perelman's work on Ricci flow and geometrization.
Author: V. M. Buchstaber
Publisher: American Mathematical Soc.
ISBN: 0821831860
Category : Combinatorial analysis
Languages : en
Pages : 154
Get Book
Book Description
Here, the study of torus actions on topological spaces is presented as a bridge connecting combinatorial and convex geometry with commutative and homological algebra, algebraic geometry, and topology. This established link helps in understanding the geometry and topology of a space with torus action by studying the combinatorics of the space of orbits. Conversely, subtle properties of a combinatorial object can be realized by interpreting it as the orbit structure for a propermanifold or as a complex acted on by a torus. The latter can be a symplectic manifold with Hamiltonian torus action, a toric variety or manifold, a subspace arrangement complement, etc., while the combinatorial objects include simplicial and cubical complexes, polytopes, and arrangements. This approachalso provides a natural topological interpretation in terms of torus actions of many constructions from commutative and homological algebra used in combinatorics. The exposition centers around the theory of moment-angle complexes, providing an effective way to study invariants of triangulations by methods of equivariant topology. The book includes many new and well-known open problems and would be suitable as a textbook. It will be useful for specialists both in topology and in combinatoricsand will help to establish even tighter connections between the subjects involved.
Author: S. G. Dani
Publisher: Springer Nature
ISBN: 3030136094
Category : Mathematics
Languages : en
Pages : 759
Get Book
Book Description
This is a collection of surveys on important mathematical ideas, their origin, their evolution and their impact in current research. The authors are mathematicians who are leading experts in their fields. The book is addressed to all mathematicians, from undergraduate students to senior researchers, regardless of the specialty.
Author: Gregory L. Naber
Publisher: Springer Science & Business Media
ISBN: 1441972544
Category : Mathematics
Languages : en
Pages : 454
Get Book
Book Description
Like any books on a subject as vast as this, this book has to have a point-of-view to guide the selection of topics. Naber takes the view that the rekindled interest that mathematics and physics have shown in each other of late should be fostered, and that this is best accomplished by allowing them to cohabit. The book weaves together rudimentary notions from the classical gauge theory of physics with the topological and geometrical concepts that became the mathematical models of these notions. The reader is asked to join the author on some vague notion of what an electromagnetic field might be, to be willing to accept a few of the more elementary pronouncements of quantum mechanics, and to have a solid background in real analysis and linear algebra and some of the vocabulary of modern algebra. In return, the book offers an excursion that begins with the definition of a topological space and finds its way eventually to the moduli space of anti-self-dual SU(2) connections on S4 with instanton number -1.
Author: Peter W. Michor
Publisher: American Mathematical Soc.
ISBN: 0821820036
Category : Geometry, Differential
Languages : en
Pages : 510
Get Book
Book Description
"This book treats the fundamentals of differential geometry: manifolds, flows, Lie groups and their actions, invariant theory, differential forms and de Rham cohomology, bundles and connections, Riemann manifolds, isometric actions, and symplectic and Poisson geometry. It gives the careful reader working knowledge in a wide range of topics of modern coordinate-free differential geometry in not too many pages. A prerequisite for using this book is a good knowledge of undergraduate analysis and linear algebra."--BOOK JACKET.
Author: Ethan D. Bloch
Publisher: Springer Science & Business Media
ISBN: 0817681221
Category : Mathematics
Languages : en
Pages : 433
Get Book
Book Description
The uniqueness of this text in combining geometric topology and differential geometry lies in its unifying thread: the notion of a surface. With numerous illustrations, exercises and examples, the student comes to understand the relationship of the modern abstract approach to geometric intuition. The text is kept at a concrete level, avoiding unnecessary abstractions, yet never sacrificing mathematical rigor. The book includes topics not usually found in a single book at this level.
Author: Josi A. de Azcárraga
Publisher: Cambridge University Press
ISBN: 9780521597005
Category : Mathematics
Languages : en
Pages : 480
Get Book
Book Description
A self-contained introduction to the cohomology theory of Lie groups and some of its applications in physics.
Author: Wang Rong
Publisher: World Scientific
ISBN: 9814495808
Category : Mathematics
Languages : en
Pages : 222
Get Book
Book Description
This book gives an outline of the developments of differential geometry and topology in the twentieth century, especially those which will be closely related to new discoveries in theoretical physics.
