MATH6072 - Topics in Topology II - 2023/24

Announcement

• Classes currently meet via Zoom. Email yjlee@ims.cuhk.edu.hk for the Zoom link.

Textbooks

• Ozsváth-Szabó, "An introduction to Heegaard Floer homology", in Floer homology, gauge theory, and low dimensional topology, 3-27, AMS, 2006.
• Ozsváth-Szabó, "Lectures on Heegaard Floer homology", in Floer homology, gauge the-ory, and low dimensional topology, 29-70, AMS, 2006.
• Ozsváth-Szabó, "Heegaard diagrams and holomorphic disks", in Different faces of geometry, 301-348, Kluwer/Plenum, New York, 2004.
• C. Manolescu, "An introduction to knot Floer homology", in Physics and mathematics of link homology, 99-135, Contemp. Math. 680, AMS, 2016.
• J. Hom, "A survery on Heegaard Floer homology and concordance", J. Knot Theory Ramifications 26 (2017), no. 2, 1740015, 24 pp.

References

• Ozsváth-Szabó, "Holomorphic disks and topological invariants for closed three-manifolds", Ann. Math.
• Ozsváth-Szabó, "Holomorphic disks and three-manifold invariants: properties and applications", Ann. Math.
• Robert Lipshitz, "A cylindrical reformulation of Heegaard Floer homology", Geom. Top.
• Ozsváth-Szabó, "Absolutely Graded Floer homologies and intersection forms for four-manifolds with boundary"
• McDuff & Salamon, Introduction to Symplectic Topology.
• McDuff & Salamon, J-holomorphic Curves and Symplectic Topology.

Assessment Scheme

Useful Links

• Ozsváth and Szabó, "An Introduction to Heegaard Floer Homology"
• Ozsváth and Szabó, "Lectures on Heegaard Floer Homology"
• Ozsváth and Szabó, "Heegaard Diagrams and Holomorphic Disks"
• J. Hom, "Lecture notes on Heegaard Floer homology"