A family of cohomological complex projective spaces

TL;DR

This paper introduces a family of complex manifolds that share cohomology with complex projective spaces across odd dimensions but are not homotopy equivalent, and also explores their even-dimensional counterparts.

Contribution

It constructs new examples of complex manifolds with cohomology matching projective spaces, expanding understanding of their topological distinctions.

Findings

Family exists for each odd complex dimension

Manifolds share cohomology with projective spaces

Not homotopy equivalent to standard projective spaces

Abstract

We exhibit a family of complex manifolds, which has a member at each odd complex dimension and which has the same cohomology groups as the complex projective space at that dimension, but not homotopy equivalent to it. We also analyze the even dimensional analogue.