Lecture Hall 5F, Cosmology Building, NTU

(臺灣大學宇宙學大樓 五樓演講廳)

Associative Submanifolds of the Berger Space

Jesse Madnick (NCTS)

Abstract:

In complex geometry, given a special Lagrangian cone in a Calabi-Yau cone (e.g., R^6), its link is a minimal Legendrian in a Sasaki-Einstein manifold (e.g., S^5). Similarly, in the theory of exceptional holonomy, given a Cayley cone in a Spin(7)-holonomy cone (e.g., R^8), its link is a (minimal) “associative 3-fold” in a “nearly-parallel 7-manifold” (e.g., S^7). In this talk (joint work with Gavin Ball), we consider the Berger space B^7 = SO(5)/SO(3) — a positively-curved compact 7-manifold with a homogeneous nearly-parallel structure — and construct the first complete associative 3-folds in B. Our examples are circle bundles over genus g surfaces for every g ≥ 0, thus providing infinitely many topological types of compact associative 3-folds in B.