Resources

Here are some links to books, lecture notes and survey papers that cover in depth some of the topics mentioned in the blog.  Feel free to post suggestions in the comments and we’ll add them to the list.

4-manifolds, Selman Akbulut

A beginner’s guide to Fukaya categories, Denis Auroux

Stein structures: existence and flexibility, Kai Cieliebak and Yakov Eliashberg

Legendrian and transverse knots, John Etnyre

Lectures on contact geometry in low-dimensional topology, John Etnyre (covers (1) foliations and contact structures (2) symplectic handles (3) open book decompositions (4) symplectic caps)

Lectures on open books decompositions and contact structures, John Etnyre

Lectures on knot homology and quantum curves, Sergei Gukov and Ingmar Saberi

Lectures on embedded contact homology, Michael Hutchings

Notes on bordered Heegaard Floer homology, Robert Lipschitz, Peter Ozsvath, Dylan Thurston

Topological methods in 3-dimensional contact geometry, Patrick Massot (convex surface theory)

Higher dimensional contact topology via holomorphic disks, Klaus Niederkruger

A topological introduction to knot contact homology, Lenhard Ng

Geometric decompositions of almost-contact manifods, Francisco Presas

Textbooks:

From Stein to Weinstein and Back: Symplectic Geometry of Affine Complex Manifolds, Cieliebak and Eliashberg
Introduction to the $h$-Principle, Eliashberg and Mishachev
Knots and Links, Rolfsen
4-Manifolds and Kirby Calculus , Gompf and Stipsicz
Monopoles and Three-Manifolds Kronheimer and Mrowka
Introduction to Symplectic Topology McDuff and Salamon
J-Holomorphic Curves and Symplectic Topology McDuff and Salamon
Quantum Fields and Strings: A Course for Mathematicians, Deligne, Etinghof, Freed, Jeffrey, Kazhdan, Morgan, Morrison, Witten
Conformal Field Theory and Topology, Toshitake Kohno
Chern-Simons Theory, Matrix Models, and Topological Strings, Marcos Marino
Mirror symmetry, Clay Mathematics monographs
Quantum Mechanics for Mathematicians, Leon Takhtajan
Supersymmetry and Supergravity, Julius Wess and Jonathan Bagger
Introduction to Superanalysis F.A. Berezin
The Wild World of 4-Manifolds, Scorpan
Notes on Seiberg-Witten Theory, Nicolaescu

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5 responses to “Resources

  1. Pingback: Resources page | The Electric Handle Slide

  2. Hello,

    Could you add some material for connections to Physics and some beginner’s lecture notes there.

    Regards,
    Vijay

    • PLC

      I don’t know much about connections to physics, except small bits of ad-hoc intuition I’ve occasionally picked up. I found Takhtajan’s book “Quantum Mechanics for Mathematicians” to be really good. But I think connections to physics generally fall outside the scope of this blog.

  3. Khoulé Cheikh

    I am very fan with this kind of learning, i am just asking for you to add
    D. Rolfsen, Knots and Links, AMS Chelsea Publishing, AMS (1990)

  4. Pingback: Contact Hamiltonians (Introduction) | The Electric Handle Slide

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