Notes on branched coverings of Seifert manifolds

TL;DR

This paper provides detailed proofs and explicit constructions related to fiber-preserving branched coverings of Seifert manifolds, extending previous criteria for their existence and factorability.

Contribution

It supplies detailed proofs, explicit constructions, and demonstrates factorability of fiber-preserving branched coverings between Seifert manifolds.

Findings

Explicit construction of fiber-preserving branched coverings for Seifert fibered solid tori

Criteria for the existence of such coverings based on Seifert invariants

Proof of factorability of coverings between closed Seifert manifolds

Abstract

In a paper published in 2002, the author gave a criterion to determine whether there is a fiber-preserving branched covering between two given orientable Seifert manifolds with orientable bases. Here we supply some details of the proof of two claims in that paper. We give an explicit construction of fiber-preserving branched covering between two Seifert fibered solid tori when their Seifert invariants satisfy certain relation, and we show the factorability of fiber-preserving branched coverings between two closed Seifert manifolds.