The integral monodromy of isolated quasihomogeneous singularities

Sasaki–Einstein 7-manifolds and Orlik’s conjecture

“…We also improve previous results given by Boyer [12] showing new examples of Sasaki-Einstein 2-connected 7-manifolds homeomorphic to connected sums of S 3 × S 4 . Actually we show that manifolds of the form #k S 3 × S 4 admit Sasaki-Einstein metrics for 22 different values of k. All these links arise as Thom-Sebastiani sums of chain type singularities and cycle type singularities where Orlik's conjecture holds due to a recent result by Hertling and Mase [19].…”

“…In this paper we benefit from a recent result by Hertling and Mase in [19] where they show that the Orlik conjecture is valid for chain type singularities, cycle type singularities and Thom-Sebastiani sums of them, and we improve results given in [6], [12] and [18]. From the list of 1936 Sasaki-Einstein 7-manifolds realized as links from the list given in [6,21] we detect 1673 that are links of hypersurface singularities of these types.…”

“…This conjecture was known to hold in certain special cases [27]. In a rather recent paper, Hertling and Mase [19], extend the list of possible cases and showed that this conjecture is true for the following cases:…”