Grid Homology for Knots and Links - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Grid Homology for Knots and Links write by Peter S. Ozsváth. This book was released on 2015-12-04. Grid Homology for Knots and Links available in PDF, EPUB and Kindle. Knot theory is a classical area of low-dimensional topology, directly connected with the theory of three-manifolds and smooth four-manifold topology. In recent years, the subject has undergone transformative changes thanks to its connections with a number of other mathematical disciplines, including gauge theory; representation theory and categorification; contact geometry; and the theory of pseudo-holomorphic curves. Starting from the combinatorial point of view on knots using their grid diagrams, this book serves as an introduction to knot theory, specifically as it relates to some of the above developments. After a brief overview of the background material in the subject, the book gives a self-contained treatment of knot Floer homology from the point of view of grid diagrams. Applications include computations of the unknotting number and slice genus of torus knots (asked first in the 1960s and settled in the 1990s), and tools to study variants of knot theory in the presence of a contact structure. Additional topics are presented to prepare readers for further study in holomorphic methods in low-dimensional topology, especially Heegaard Floer homology. The book could serve as a textbook for an advanced undergraduate or part of a graduate course in knot theory. Standard background material is sketched in the text and the appendices.
Grid Homology for Knots and Links
Grid Homology for Knots and Links - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Grid Homology for Knots and Links write by Peter S. Ozsvath. This book was released on 2017-01-19. Grid Homology for Knots and Links available in PDF, EPUB and Kindle. Knot theory is a classical area of low-dimensional topology, directly connected with the theory of three-manifolds and smooth four-manifold topology. In recent years, the subject has undergone transformative changes thanks to its connections with a number of other mathematical disciplines, including gauge theory; representation theory and categorification; contact geometry; and the theory of pseudo-holomorphic curves. Starting from the combinatorial point of view on knots using their grid diagrams, this book serves as an introduction to knot theory, specifically as it relates to some of the above developments. After a brief overview of the background material in the subject, the book gives a self-contained treatment of knot Floer homology from the point of view of grid diagrams. Applications include computations of the unknotting number and slice genus of torus knots (asked first in the 1960s and settled in the 1990s), and tools to study variants of knot theory in the presence of a contact structure. Additional topics are presented to prepare readers for further study in holomorphic methods in low-dimensional topology, especially Heegaard Floer homology. The book could serve as a textbook for an advanced undergraduate or part of a graduate course in knot theory. Standard background material is sketched in the text and the appendices.
Knots and Links
Knots and Links - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Knots and Links write by Peter R. Cromwell. This book was released on 2004-10-14. Knots and Links available in PDF, EPUB and Kindle. A richly illustrated 2004 textbook on knot theory; minimal prerequisites but modern in style and content.
The Mathematics of Knots
The Mathematics of Knots - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook The Mathematics of Knots write by Markus Banagl. This book was released on 2010-11-25. The Mathematics of Knots available in PDF, EPUB and Kindle. The present volume grew out of the Heidelberg Knot Theory Semester, organized by the editors in winter 2008/09 at Heidelberg University. The contributed papers bring the reader up to date on the currently most actively pursued areas of mathematical knot theory and its applications in mathematical physics and cell biology. Both original research and survey articles are presented; numerous illustrations support the text. The book will be of great interest to researchers in topology, geometry, and mathematical physics, graduate students specializing in knot theory, and cell biologists interested in the topology of DNA strands.
Bordered Heegaard Floer Homology
Bordered Heegaard Floer Homology - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Bordered Heegaard Floer Homology write by Robert Lipshitz. This book was released on 2018-08-09. Bordered Heegaard Floer Homology available in PDF, EPUB and Kindle. The authors construct Heegaard Floer theory for 3-manifolds with connected boundary. The theory associates to an oriented, parametrized two-manifold a differential graded algebra. For a three-manifold with parametrized boundary, the invariant comes in two different versions, one of which (type D) is a module over the algebra and the other of which (type A) is an A∞ module. Both are well-defined up to chain homotopy equivalence. For a decomposition of a 3-manifold into two pieces, the A∞ tensor product of the type D module of one piece and the type A module from the other piece is ^HF of the glued manifold. As a special case of the construction, the authors specialize to the case of three-manifolds with torus boundary. This case can be used to give another proof of the surgery exact triangle for ^HF. The authors relate the bordered Floer homology of a three-manifold with torus boundary with the knot Floer homology of a filling.
