Iterated $S^3$ Sasaki Joins and Bott Orbifolds

TL;DR

This paper explores the relationship between iterated $S^3$ Sasaki-joins and Bott orbifolds, providing explicit constructions of smooth Sasaki-Einstein structures up to dimension eleven and conjecturing their existence in all odd dimensions.

Contribution

It establishes a categorical link between Sasaki-joins and Bott orbifolds and constructs explicit smooth Sasaki-Einstein structures in multiple dimensions.

Findings

Explicit constructions up to dimension eleven.

Categorical relationship between joins and orbifolds.

Conjecture on existence in all odd dimensions.

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.