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Lectures on Quantum Topology in Dimension Three
 
Thang T. Q. Lê Georgia Institute of Technology, Atlanta, Georgia
Christine Lescop Université Grenoble Alpes, Grenoble, France
Robert Lipshitz Columbia University, New York, NY
Paul Turner Université de Genève, Geneva, Switzerland
A publication of the Société Mathématique de France
Lectures on Quantum Topology in Dimension Three
Softcover ISBN:  978-2-85629-842-8
Product Code:  PASY/48
List Price: $52.00
AMS Member Price: $41.60
Please note AMS points can not be used for this product
Lectures on Quantum Topology in Dimension Three
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Lectures on Quantum Topology in Dimension Three
Thang T. Q. Lê Georgia Institute of Technology, Atlanta, Georgia
Christine Lescop Université Grenoble Alpes, Grenoble, France
Robert Lipshitz Columbia University, New York, NY
Paul Turner Université de Genève, Geneva, Switzerland
A publication of the Société Mathématique de France
Softcover ISBN:  978-2-85629-842-8
Product Code:  PASY/48
List Price: $52.00
AMS Member Price: $41.60
Please note AMS points can not be used for this product
  • Book Details
     
     
    Panoramas et Synthèses
    Volume: 482016; 174 pp
    MSC: Primary 57

    This monograph contains three lecture series from the SMF school Geometric and Quantum Topology in Dimension 3, which was held at CIRM in June 2014. These lectures present recent progress on the study of 3-manifold and link invariants. Thang Lê describes the state of the art about the AJ conjecture, which relates generalizations of the Jones polynomial to the Cooper, Culler, Gillet, Long and Shalen A-polynomial, which is defined from \(SL_2(C)\)-representation spaces of link exterior fundamental groups.

    In 1999, Khovanov defined a homology theory for knots of \(R^3\) whose Euler characteristic is the Jones polynomial. Paul Turner presents the latest developments and the applications of this categorification of the Jones polynomial in a useful guide of the literature around this extensively studied topic. Robert Lipshitz presents the famous Osváth Szábo Heegaard Floer homology theories together with efficient sketches of proofs of some of their spectacular applications. These lectures are introduced by a partial survey of the history of these invariants, written by Christine Lescop.

    A publication of the Société Mathématique de France, Marseilles (SMF), distributed by the AMS in the U.S., Canada, and Mexico. Orders from other countries should be sent to the SMF. Members of the SMF receive a 30% discount from list.

    Readership

    Graduate students and research mathematicians interested in geometry and topology.

  • Additional Material
     
     
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Accessibility – to request an alternate format of an AMS title
Volume: 482016; 174 pp
MSC: Primary 57

This monograph contains three lecture series from the SMF school Geometric and Quantum Topology in Dimension 3, which was held at CIRM in June 2014. These lectures present recent progress on the study of 3-manifold and link invariants. Thang Lê describes the state of the art about the AJ conjecture, which relates generalizations of the Jones polynomial to the Cooper, Culler, Gillet, Long and Shalen A-polynomial, which is defined from \(SL_2(C)\)-representation spaces of link exterior fundamental groups.

In 1999, Khovanov defined a homology theory for knots of \(R^3\) whose Euler characteristic is the Jones polynomial. Paul Turner presents the latest developments and the applications of this categorification of the Jones polynomial in a useful guide of the literature around this extensively studied topic. Robert Lipshitz presents the famous Osváth Szábo Heegaard Floer homology theories together with efficient sketches of proofs of some of their spectacular applications. These lectures are introduced by a partial survey of the history of these invariants, written by Christine Lescop.

A publication of the Société Mathématique de France, Marseilles (SMF), distributed by the AMS in the U.S., Canada, and Mexico. Orders from other countries should be sent to the SMF. Members of the SMF receive a 30% discount from list.

Readership

Graduate students and research mathematicians interested in geometry and topology.

Review Copy – for publishers of book reviews
Accessibility – to request an alternate format of an AMS title
Please select which format for which you are requesting permissions.