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Smooth Blowups: Global vs. Local Perspectives

Aleksey Zinger

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.

Smooth Blowups: Global vs. Local Perspectives

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.
Paper Structure (12 sections, 7 theorems, 146 equations)

This paper contains 12 sections, 7 theorems, 146 equations.

Table of Contents

  1. Introduction
  2. Real and complex blowups
  3. Global construction
  4. Local construction
  5. Equivalence
  6. Augmented blowup
  7. Global construction
  8. Preparation
  9. Construction
  10. Open sets description
  11. Local construction
  12. Equivalence

Key Result

Theorem 1

Let $X$ be a smooth manifold and $Y\!\subset\!X$ be a closed submanifold of codimension $\mathfrak c$.

Theorems & Definitions (11)

  • Theorem
  • Lemma 2.1: RDMbl
  • Proposition 2.2
  • proof
  • Lemma 2.3
  • proof
  • Lemma 3.1: RDMbl
  • Proposition 3.2
  • proof
  • Lemma 3.3
  • ...and 1 more