Iterated $S^3$ Sasaki Joins and Bott Orbifolds

Abstract

We present a categorical relationship between iterated $S^3$ Sasaki-joins and Bott orbifolds. Then we show how to construct smooth Sasaki-Einstein (SE) structures on the iterated joins. These become increasingly complicated as dimension grows. We give an explicit construction of (infinitely many) smooth SE structures up through dimension eleven, and conjecture the existence of smooth SE structures in all odd dimensions.Comment: 19 pages, Paper submitted to the upcoming conference {\it AMAZER: Analysis of Monge-Amp\`ere, a tribute to Ahmed Zeriahi} at the Institute of Mathematics of Toulouse (June 202