On a high-dimensional generalization of Seifert fibrations

TL;DR

This paper introduces a generalized concept of Seifert fibrations, demonstrates their realization on specific Eschenburg 7-manifolds, and defines associated characteristic classes, expanding the understanding of high-dimensional fibered structures.

Contribution

It presents a new generalization of Seifert fibrations and applies it to certain Eschenburg manifolds, defining their characteristic classes.

Findings

Proposed a generalized Seifert fibration concept.

Identified fibrations on Eschenburg 7-manifolds.

Defined characteristic classes for these fibrations.

Abstract

The notion of generalized Seifert fibration is introduced, it is shown that the projections of certain Eschenburg $7$-manifolds onto ${\mathbb C} P^2$ define such fibrations, and for them the characteristic classes corresponding to the generators of $H^2(B(U(2)/{\mathbb Z}_{2n});{\mathbb Z})$ are defined.