Geometry & Topology Seminar

Friday, April 22, 2022 2:30 pm - 2:30 pm EDT (GMT -04:00)

Jesse Madnick, National Taiwan University

"Associative 3-folds in Squashed 7-Spheres"

The quaternionic Hopf fibration S7 → S4 lets us view the round 7-sphere as a family of round 3-spheres.  Dilating these 3-spheres by t > 0 yields a family of Riemannian 7-manifolds S7(t) called “squashed 7-spheres.”  Each of these spaces admits a natural (highly symmetric) co-closed G2-structure, making the squashed 7-spheres fundamental examples in G2-geometry. In this talk, we construct the first non-trivial compact associative 3-folds in S7(t) for every t > 0.  Our examples arise from “twisting” circle bundles over pseudo-holomorphic curves in CP3 by a meromorphic function. Time permitting, we explain how our construction generalizes to the larger class of "squashed" 3-Sasakian 7-manifolds.  This is joint work with Gavin Ball.

This seminar will be held jointly online and in person: