Jonathan C. Johnson

Office: MSCS 524
Department of Mathematics
Oklahoma State University

Knot Concordance

This is the web page for the learning seminar about knot concordance. Knot concordance is an exciting theory in the intersection of three-manifold and four-manifold topology (often called 3.5-dimentional). Int this seminar we will read parts of Livingston and Naik's book, then work through a couple of papers including a result of Abe and Tagami.


References for Talks
  Abe and Tagami, "Fibered knots with the same 0-surgeries and the slice-ribbon conjecture" (2016)
  Gordon, "Ribbon concordance of knots in the 3-sphere" (1981)
  Livingston and Naik, "Introduction to knot concordance" (unpublished)
  Miller and Piccirillo, Knot traces and concordance
  Miyazaki;, "Nonsimple, ribbon fibered knots" (1994)

Other References
  Gompf and Miyazaki, Some well disguised ribbon knots
  Yasui, Corks, exotic 4-manifolds and knot concordance (go to the end of the page)


This seminar meets in RLM 12.166 at 2:00pm. Here's the tentative schedule for this seminar.:

January 24: Introduction and Organizational Meeting(Jonathan)

January 31: Handle Decomposition and Morse Theory(Jonathan)
  Resource: Livingston and Naik, Section 2.2

February 7: Knot Concordance(Shiyu)
  Resource: Livingston and Naik, Sections 3.1, 3.2, and 3.3

February 14: Annulus Twists(Hannah)
  Resource: Abe and Tagami, Sections 1 and 5

February 21: Ribbon Concordance(Alexandra)
  Resource: Gordon, Sections 1, 2, and 3

February 28: Ribbon Fibered Knots(Kai)
  Resource: Abe and Tagami, Sections 2 and 4
  Also, Miyazaki, Sections 1 and 5

March 27: Dualizable Patterns(Jonathan) (video)
  Resource: Miller and Piccirillo, Section 3

April 3: 0-Surgeries and 0-Traces (video)
  Resource: Miller and Piccirillo, Section 4

April 17: d-Invariants (video)
  Resource: Miller and Piccirillo, Sections 5 and 7

April 24: Relationship to Annulus Twisting (video)
  Resource: Miller and Piccirillo, Section 6