0-Concordance of 2-Knots

Geometry Topology Student Seminar
Wednesday, September 4, 2019 - 2:00pm for 1 hour (actually 50 minutes)
Skiles 006
Anubhav Mukherjee
Agniva Roy

 A 2-knot is a smooth embedding of S^2 in S^4, and a 0-concordance of 2-knots is a concordance with the property that every regular level set of the concordance is just a collection of S^2's. In his thesis, Paul Melvin proved that if two 2-knots are 0-concordant, then a Gluck twist along one will result in the same smooth 4-manifold as a Gluck twist on the other. He asked the following question: Are all 2-knots 0-slice (i.e. 0-concordant to the unknot)? I will explain all relevant definitions, and mostly follow the paper by Nathan Sunukjian on this topic.