Iterated $S^3$ Sasaki Joins and Bott Orbifolds

Boyer, Charles P.; Tønnesen-Friedman, Christina W.

Annales de la Faculté des sciences de Toulouse : Mathématiques, Série 6, Tome 31 (2022) no. 3, pp. 837-860.

Nous présentons une relation catégorique entre les jointures Sasaki $S^3$ itérées et les orbifolds Bott. Ensuite, nous montrons comment construire des structures Sasaki–Einstein (SE) lisses sur les jointures itérées. Celles-ci deviennent de plus en plus compliquées à mesure que la dimension augmente. Nous donnons une construction non triviale explicite de structures SE lisses (infiniment nombreuses) jusqu’à la dimension onze, et conjecturons l’existence de structures SE lisses dans toutes les dimensions impaires.

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 nontrivial construction of (infinitely many) smooth SE structures up through dimension eleven, and conjecture the existence of smooth SE structures in all odd dimensions.

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