Joint GT-UGA Seminar at GT: Gluck twists and trisections

Geometry Topology Seminar
Monday, March 13, 2017 - 15:30
1 hour (actually 50 minutes)
Skiles 006
This is joint work with Jeff Meier. The Gluck twist operation removes an S^2XB^2 neighborhood of a knotted S^2 in S^4 and glues it back with a twist, producing a homotopy S^4 (i.e. potential counterexamples to the smooth Poincare conjecture, although for many classes of 2-knots theresults are in fact known to be smooth S^4's). By representing knotted S^2's in S^4 as doubly pointed Heegaard triples and understanding relative trisection diagrams of S^2XB^2 carefully, I'll show how to produce trisection diagrams (a.k.a. Heegaard triples) for these homotopy S^4's.(And for those not up on trisections I'll review the foundations.) The resulting recipe is surprisingly simple, but the fun, as always, is in the process.