A Knot Bounding a Grope of Class N is [n/2]- Trivial
Author: James Roger Conant
Publisher:
Published: 2000
Total Pages: 138
ISBN-13:
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2-Knots and Their Groups
Author: Jonathan Hillman
Publisher: CUP Archive
Published: 1989-03-30
Total Pages: 180
ISBN-13: 9780521378123
DOWNLOAD EBOOKTo attack certain problems in 4-dimensional knot theory the author draws on a variety of techniques, focusing on knots in S^T4, whose fundamental groups contain abelian normal subgroups. Their class contains the most geometrically appealing and best understood examples. Moreover, it is possible to apply work in algebraic methods to these problems. Work in four-dimensional topology is applied in later chapters to the problem of classifying 2-knots.
Geometry and Topology of Manifolds
Author: Hans U. Boden
Publisher: American Mathematical Soc.
Published: 2005
Total Pages: 362
ISBN-13: 0821837249
DOWNLOAD EBOOKThis book contains expository papers that give an up-to-date account of recent developments and open problems in the geometry and topology of manifolds, along with several research articles that present new results appearing in published form for the first time. The unifying theme is the problem of understanding manifolds in low dimensions, notably in dimensions three and four, and the techniques include algebraic topology, surgery theory, Donaldson and Seiberg-Witten gauge theory,Heegaard Floer homology, contact and symplectic geometry, and Gromov-Witten invariants. The articles collected for this volume were contributed by participants of the Conference "Geometry and Topology of Manifolds" held at McMaster University on May 14-18, 2004 and are representative of the manyexcellent talks delivered at the conference.
Methods of Functional Analysis and Topology
Author:
Publisher:
Published: 2004
Total Pages: 390
ISBN-13:
DOWNLOAD EBOOKGroup Theory From A Geometrical Viewpoint
Author: Alberto Verjovski
Publisher: #N/A
Published: 1991-08-12
Total Pages: 744
ISBN-13: 981456964X
DOWNLOAD EBOOKThis proceedings presents the latest research materials done on group theory from geometrical viewpoint in particular Gromov's theory of hyperbolic groups, Coxeter groups, Tits buildings and actions on real trees. All these are very active subjects.
Lecture Notes On Knot Invariants
Author: Weiping Li
Publisher: World Scientific
Published: 2015-08-21
Total Pages: 245
ISBN-13: 9814675989
DOWNLOAD EBOOKThe volume is focused on the basic calculation skills of various knot invariants defined from topology and geometry. It presents the detailed Hecke algebra and braid representation to illustrate the original Jones polynomial (rather than the algebraic formal definition many other books and research articles use) and provides self-contained proofs of the Tait conjecture (one of the big achievements from the Jones invariant). It also presents explicit computations to the Casson-Lin invariant via braid representations.With the approach of an explicit computational point of view on knot invariants, this user-friendly volume will benefit readers to easily understand low-dimensional topology from examples and computations, rather than only knowing terminologies and theorems.
Knot Theory
Author: Vassily Olegovich Manturov
Publisher: CRC Press
Published: 2018-04-17
Total Pages: 560
ISBN-13: 1351359134
DOWNLOAD EBOOKOver the last fifteen years, the face of knot theory has changed due to various new theories and invariants coming from physics, topology, combinatorics and alge-bra. It suffices to mention the great progress in knot homology theory (Khovanov homology and Ozsvath-Szabo Heegaard-Floer homology), the A-polynomial which give rise to strong invariants of knots and 3-manifolds, in particular, many new unknot detectors. New to this Edition is a discussion of Heegaard-Floer homology theory and A-polynomial of classical links, as well as updates throughout the text. Knot Theory, Second Edition is notable not only for its expert presentation of knot theory’s state of the art but also for its accessibility. It is valuable as a profes-sional reference and will serve equally well as a text for a course on knot theory.
Advances in Two-Dimensional Homotopy and Combinatorial Group Theory
Author: Wolfgang Metzler
Publisher: Cambridge University Press
Published: 2017-11-16
Total Pages: 193
ISBN-13: 1108644236
DOWNLOAD EBOOKThis volume presents the current state of knowledge in all aspects of two-dimensional homotopy theory. Building on the foundations laid a quarter of a century ago in the volume Two-dimensional Homotopy and Combinatorial Group Theory (LMS 197), the editors here bring together much remarkable progress that has been obtained in the intervening years. And while the fundamental open questions, such as the Andrews–Curtis Conjecture and the Whitehead asphericity problem remain to be (fully) solved, this book will provide both students and experts with an overview of the state of the art and work in progress. Ample references are included to the LMS 197 volume, as well as a comprehensive bibliography bringing matters entirely up to date.
The Structure of the Rational Concordance Group of Knots
Author: Jae Choon Cha
Publisher: American Mathematical Soc.
Published: 2007
Total Pages: 114
ISBN-13: 0821839934
DOWNLOAD EBOOKThe author studies the group of rational concordance classes of codimension two knots in rational homology spheres. He gives a full calculation of its algebraic theory by developing a complete set of new invariants. For computation, he relates these invariants with limiting behaviour of the Artin reciprocity over an infinite tower of number fields and analyzes it using tools from algebraic number theory. In higher dimensions it classifies the rational concordance group of knots whose ambient space satisfies a certain cobordism theoretic condition. In particular, he constructs infinitely many torsion elements. He shows that the structure of the rational concordance group is much more complicated than the integral concordance group from a topological viewpoint. He also investigates the structure peculiar to knots in rational homology 3-spheres. To obtain further nontrivial obstructions in this dimension, he develops a technique of controlling a certain limit of the von Neumann $L 2$-signature invariants.
Low-dimensional and Symplectic Topology
Author: Michael Usher
Publisher: American Mathematical Soc.
Published: 2011
Total Pages: 242
ISBN-13: 0821852353
DOWNLOAD EBOOKEvery eight years since 1961, the University of Georgia has hosted a major international topology conference aimed at disseminating important recent results and bringing together researchers at different stages of their careers. This volume contains the proceedings of the 2009 conference, which includes survey and research articles concerning such areas as knot theory, contact and symplectic topology, 3-manifold theory, geometric group theory, and equivariant topology. Among other highlights of the volume, a survey article by Stefan Friedl and Stefano Vidussi provides an accessible treatment of their important proof of Taubes' conjecture on symplectic structures on the product of a 3-manifold and a circle, and an intriguing short article by Dennis Sullivan opens the door to the use of modern algebraic-topological techniques in the study of finite-dimensional models of famously difficult problems in fluid dynamics. Continuing what has become a tradition, this volume contains a report on a problem session held at the conference, discussing a variety of open problems in geometric topology.
