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.
Resources
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Livingston and Naik, "Introduction to knot concordance" (unpublished)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)
Schedule
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