Grid homology for knots and links / Peter S. Ozsváth, András I. Stipsicz, Zoltán Szabó.

Format:

Book

Author/Creator:

Ozsváth, Peter Steven, 1967- author.

Stipsicz, András, author.

Szabó, Zoltán, 1965- author.

Series:

Mathematical surveys and monographs ; no. 208.

Mathematical surveys and monographs ; volume 208

Language:

English

Subjects (All):

Knot theory.

Link theory.

Homology theory.

Physical Description:

x, 410 pages : illustrations ; 27 cm.

Place of Publication:

Providence, Rhode Island : American Mathematical Society, [2015]

Summary:

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.

Contents:

Introduction

Knots and links in S³

Grid diagrams

Grid homology

The invariance of grid homology

The unknotting number and tau

Basic properties of grid homology

The slice genus and tau

The oriented skein exact sequence

Grid homologies of alternating knots

Grid homology for links

Invariants of Legendrian and transverse knots

The filtered grid complex

More on the filtered chain complex

Grid homology over the integers

The holomorphic theory

Open problems.

Notes:

Includes bibliographical references (pages 399-406) and index.

ISBN:

9781470417376

1470417375

OCLC:

915323944