On the Topology of some Sasaki-Einstein Manifolds

TL;DR

This paper explores the topological properties of Sasaki-Einstein manifolds, explicitly computing cohomology rings and providing homotopy equivalence formulas for specific cases, advancing understanding of their geometric structure.

Contribution

It extends previous work by explicitly calculating cohomology rings for new cases and deriving a homotopy equivalence formula in a 7-dimensional example.

Findings

Computed cohomology rings for new Sasaki-Einstein manifolds

Derived a homotopy equivalence formula in a 7-dimensional case

Enhanced understanding of the topological classification of these manifolds

Abstract

This is a sequel to our paper arXiv:1402.2546 to appear in the Journal of Geometric Analysis in which we concentrate on developing some of the topological properties of Sasaki-Einstein manifolds. In particular, we explicitly compute the cohomology rings for several cases not treated in arXiv:1402.2546 and give a formula for homotopy equivalence in one particular 7-dimensional case.