Smooth Blowups: Global vs. Local Perspectives

TL;DR

This paper demonstrates the equivalence of global and local constructions of three types of blowups in smooth manifolds, clarifying their relationship in differential topology.

Contribution

It establishes the equivalence between global and local blowup constructions for three types in smooth manifolds, providing a unified perspective.

Findings

Global and local blowups are equivalent for the three types studied.

The results unify different approaches to blowups in differential topology.

This equivalence simplifies understanding of blowup constructions.

Abstract

We show that the global and local constructions of three types of blowup of a smooth manifold along a closed submanifold in differential topology are equivalent.