Resolution of singular fibers of an $S^1$-manifold

TL;DR

This paper develops a method to resolve singular fibers in 5-manifolds with circle actions and shows it aligns with resolving cyclic surface singularities in the quotient space.

Contribution

It introduces a construction for resolving discrete singular fibers in 5-manifolds with $S^1$-actions and demonstrates compatibility with cyclic surface singularity resolutions.

Findings

Resolution construction for singular fibers in 5-manifolds.

Compatibility with cyclic surface singularity resolution.

Advancement in understanding $S^1$-manifold singularities.

Abstract

In this paper, we present a construction of resolution of discrete singular fibers of a closed $5$-manifold that admits a locally free $S^1$-action, and prove its compatibility with the resolution of cyclic surface singularities in the quotient space by the $S^1$-action.