Concordance and Sliceness

Resources

Although there is no fixed text for the course, we will provide most course materials here. Lecture recordings can be found on our NextCloud using the password given in class.
Course materials
Lecture notes (single pdf)
  1. Overview and logistics (link)
  2. Definitions and examples (link)
  3. Algebraic concordance part I (link)
  4. Algebraic concordance part II; Intersection and linking forms (link)
  5. Alexander modules, Blanchfield forms, definition of Casson Gordon signature (link)
  6. Branched covers and Casson Gordon signatures as sliceness obstructions (link)
  7. (Buildup to) Alexander polynomial 1 knots are topologically slice (link)
  8. Slice-Bennequin inequalities (link)
  9. Khovanov homology (link)
  10. Lee homology and the s-invariant (link)
  11. Alexander polynomial 1 knots are topologically slice; Obstructions from Donaldson (link)
  12. Special topics (link)
  13. Open problems (link)

Additional Resources

Textbooks, notes, and et cetera
  • Ray: Slice knots and knot concordance (notes, link)
  • Rolfsen: Knots and Links (textbook, link)
  • Livingston and Naik: Introduction to knot concordance (textbook, link)
  • Livingston: A survey of classical knot concordance (notes, link)
  • Conway: Algebraic concordance and the Casson-Gordon invariants (notes, link)
  • Teichner: Slice Knots - Knot Theory in the 4th Dimension (notes, link)
  • Ruppik: Concordance of knots and links (webpage, link)
  • Lickorish: An Introduction to Knot Theory (textbook, link)
Papers
  • Quasipositivity as an obstruction to sliceness by Lee Rudolph (link)
  • On Khovanov's categorification of the Jones polynomial by Dror Bar-Natan (link)
  • Khovanov homology and the slice genus by Jacob A. Rasmussen (link)