The Andrews-Curtis Conjecture and new handle decompositions of the 4-sphere

Triangle Topology Seminar

Alex Zupan (University of Nebraska-Lincoln)

Tuesday, April 25, 2017 -
3:00pm to 4:00pm
NCSU, SAS 1102

The Andrews-Curtis Conjecture, proposed in the 1960s, asserts that every balanced presentation of the trivial group can be simplified with a set of moves, called Andrew-Curtis moves. Every handle decomposition of the 4-sphere with no 3-handles induces such a presentation, with handle-slides corresponding to Andrews-Curtis moves. The most prominent examples in this setting are due to Gompf-Scharlemann-Thompson, building off work of Akbulut-Kirby. We describe a new construction that generalizes the work of Gompf-Scharlemann-Thompson, with intriguing connections to the Andrews-Curtis Conjecture. This is joint work in progress with Jeffrey Meier.