Nous présentons une relation catégorique entre les jointures Sasaki 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 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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@article{AFST_2022_6_31_3_837_0,
author = {Charles P. Boyer and Christina W. T{\o}nnesen-Friedman},
title = {Iterated $S^3$ {Sasaki} {Joins} and {Bott} {Orbifolds}},
journal = {Annales de la Facult\'e des sciences de Toulouse : Math\'ematiques},
pages = {837--860},
publisher = {Universit\'e Paul Sabatier, Toulouse},
volume = {Ser. 6, 31},
number = {3},
year = {2022},
doi = {10.5802/afst.1706},
language = {en},
url = {https://afst.centre-mersenne.org/articles/10.5802/afst.1706/}
}
TY - JOUR AU - Charles P. Boyer AU - Christina W. Tønnesen-Friedman TI - Iterated $S^3$ Sasaki Joins and Bott Orbifolds JO - Annales de la Faculté des sciences de Toulouse : Mathématiques PY - 2022 SP - 837 EP - 860 VL - 31 IS - 3 PB - Université Paul Sabatier, Toulouse UR - https://afst.centre-mersenne.org/articles/10.5802/afst.1706/ DO - 10.5802/afst.1706 LA - en ID - AFST_2022_6_31_3_837_0 ER -
%0 Journal Article %A Charles P. Boyer %A Christina W. Tønnesen-Friedman %T Iterated $S^3$ Sasaki Joins and Bott Orbifolds %J Annales de la Faculté des sciences de Toulouse : Mathématiques %D 2022 %P 837-860 %V 31 %N 3 %I Université Paul Sabatier, Toulouse %U https://afst.centre-mersenne.org/articles/10.5802/afst.1706/ %R 10.5802/afst.1706 %G en %F AFST_2022_6_31_3_837_0
Charles P. Boyer; Christina W. Tønnesen-Friedman. Iterated $S^3$ Sasaki Joins and Bott Orbifolds. Annales de la Faculté des sciences de Toulouse : Mathématiques, Série 6, Tome 31 (2022) no. 3, pp. 837-860. doi : 10.5802/afst.1706. https://afst.centre-mersenne.org/articles/10.5802/afst.1706/
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