On irregular Sasaki-Einstein metrics in dimension 5

TL;DR

This paper proves the non-existence of irregular Sasaki-Einstein structures on rational homology 5-spheres and demonstrates the existence of continuous families of such structures on certain connected sums of S^2 x S^3 using K-stability.

Contribution

It establishes the non-existence of irregular Sasaki-Einstein structures on rational homology 5-spheres and constructs new examples on connected sums of S^2 x S^3 via K-stability.

Findings

No irregular Sasaki-Einstein structures on rational homology 5-spheres.

Existence of continuous families of irregular Sasaki-Einstein structures on S^2 x S^3 sums.

Use of K-stability to prove existence.

Abstract

We show that there are no irregular Sasaki-Einstein structures on rational homology 5-spheres. On the other hand, using K-stability we prove the existence of continuous families of non-toric irregular Sasaki-Einstein structures on odd connected sums of $S^2 \times S^3$.