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The configuration category of a covering space

Pedro Boavida de Brito, Michael S. Weiss

Abstract

We investigate the relationship between the configuration category of a manifold and the configuration category of a covering space of that manifold.

The configuration category of a covering space

Abstract

We investigate the relationship between the configuration category of a manifold and the configuration category of a covering space of that manifold.
Paper Structure (8 sections, 13 theorems, 42 equations)

This paper contains 8 sections, 13 theorems, 42 equations.

Table of Contents

  1. Introduction
  2. Statement of results
  3. Lifting configurations
  4. Unique path lifting from a categorical viewpoint
  5. Breaking the shackles
  6. Lifting maps between configuration categories
  7. Localized configurations
  8. First order coherence in towers

Key Result

Theorem 1.1

There is a dashed arrow \xymatrix@C=30pt{ q^*\textup{emb}^t(L,M) \ar[d] \ar[r]^-{(\ref{eqn-watchout})} & \textup{emb}^t(E_L,E_M) \ar[d] \\ q^*\mathbb R\textup{map}_{\mathsf{Fin}}(\mathsf{con}(L),\mathsf{con}(M)) \ar@{..>}[r] & \mathbb R\textup{map}_{\mathsf{Fin}}(\mathsf{con}(E_L),\mathsf{con}(E_M))

Theorems & Definitions (19)

  • Theorem 1.1
  • Definition 2.1
  • Definition 2.2
  • Definition 3.1
  • Proposition 3.2
  • Corollary 3.3
  • Lemma 3.4
  • Lemma 3.5
  • Proposition 3.6
  • Theorem 4.1
  • ...and 9 more