Beglund-H\"ubsch transpose and Sasaki-Einstein rational homology 7-spheres
Abstract
We show that links of invertible polynomials coming from the Johnson and Koll\'ar list of K\"ahler-Einstein 3-folds that are rational homology 7-spheres remain rational homology 7-spheres under the so-called Berglund-H\"ubsch transpose rule coming from classical mirror symmetry constructions. Actually, this rule produces twins, that is, links with same degree, Milnor number and homology H_3, with the exception of iterated Thom-Sebastiani sums of singularities of chain and cycle type, where the torsion and the Milnor number may vary. The Berglund-H\"ubsch transpose rule not only gives a framework to better understand the existence of SasakiEinstein twins but also gives a mechanism for producing new examples of Sasaki-Einstein twins in the rational homology 7 -sphere setting. We also give reasonable conditions for a Sasaki-Einstein rational homology 7-sphere to remain Sasaki-Einstein under the BH-transpose rule. In particular, we found 75 new examples of Sasaki-Einstein rational homology 7-spheres arising as links of not well-formed hypersurface singularities.
Keywords
Cite
@article{arxiv.2311.15998,
title = {Beglund-H\"ubsch transpose and Sasaki-Einstein rational homology 7-spheres},
author = {Jaime Cuadros Valle and Ralph R. Gomez and Joe Lope Vicente},
journal= {arXiv preprint arXiv:2311.15998},
year = {2024}
}
Comments
We have changed the title, corrected minor typos and added Remark 4.2