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Packing Meets Topology

Michael H. Freedman

Abstract

This note initiates an investigation of packing links into a region of Euclidean space to achieve a maximal density subject to geometric constraints. The upper bounds obtained apply only to the class of homotopically essential links and even there seem extravagantly large, leaving much working room for the interested reader.

Packing Meets Topology

Abstract

This note initiates an investigation of packing links into a region of Euclidean space to achieve a maximal density subject to geometric constraints. The upper bounds obtained apply only to the class of homotopically essential links and even there seem extravagantly large, leaving much working room for the interested reader.
Paper Structure (3 sections, 7 theorems, 7 equations)

This paper contains 3 sections, 7 theorems, 7 equations.

Table of Contents

  1. Introduction and Theorems
  2. Discussion
  3. Acknowledgements

Key Result

Theorem 1

If $H^n$ has a diagonal-$\epsilon$-embedding into the unit cube then $n(\epsilon) = O\left(e^{a\epsilon^{-3}}\right)$ for some $a > 0$.

Theorems & Definitions (14)

  • Theorem 1
  • proof
  • Theorem 2
  • proof
  • Theorem 3: Burnside
  • Definition
  • Lemma 4
  • proof
  • Lemma 5
  • proof
  • ...and 4 more