Description

Book Synopsis
Starting from the combinatorial point of view on knots using their grid diagrams, this book serves as an introduction to knot theory. 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.

Table of Contents
  • Introduction
  • Knots and links in $S^3$
  • 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
  • Homological algebra
  • Basic theorems in knot theory
  • Bibliography
  • Index

Grid Homology for Knots and Links

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    RRP £11,300.00 – you save £10,300.01 (91%)

    A Paperback by Peter S. Ozsváth, Andras I. Stipsicz, Zoltán Szabó

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      Publisher: MP-AMM American Mathematical
      Publication Date: Publication Date: 11/30/2015 12:00:00 AM
      ISBN13: 9781470434427, 978-1470434427
      ISBN10: 1470434423

      Description

      Book Synopsis
      Starting from the combinatorial point of view on knots using their grid diagrams, this book serves as an introduction to knot theory. 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.

      Table of Contents
      • Introduction
      • Knots and links in $S^3$
      • 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
      • Homological algebra
      • Basic theorems in knot theory
      • Bibliography
      • Index

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