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On the group of homotopy classes of relative homotopy automorphisms

Hadrien Espic, Bashar Saleh

Abstract

We prove that the group of homotopy classes of relative homotopy automorphisms of a simply connected finite CW-complex is finitely presented and that the rationalization map from this group to its rational analogue has a finite kernel.

On the group of homotopy classes of relative homotopy automorphisms

Abstract

We prove that the group of homotopy classes of relative homotopy automorphisms of a simply connected finite CW-complex is finitely presented and that the rationalization map from this group to its rational analogue has a finite kernel.

Paper Structure

This paper contains 6 sections, 24 theorems, 47 equations.

Table of Contents

  1. Introduction
  2. Finite kernel
  3. On minimal relative dg Lie algebras
  4. Algebraic groups and relative homotopy automorphisms
  5. Finite presentation
  6. Finite Postnikov stages

Key Result

Theorem 1.1

Let $A\subset X$ be a cofibration of simply connected spaces of the homotopy type of finite CW-complexes. Then $\pi_0(\mathop{\mathrm{aut}}\nolimits_A(X))$ is finitely presented and the map $\pi_0(\mathop{\mathrm{aut}}\nolimits_A(X))\to \pi_0(\mathop{\mathrm{aut}}\nolimits_{A_\mathbb{Q}}(X_\mathbb{Q

Theorems & Definitions (55)

  • Theorem 1.1
  • Theorem 1.2
  • Theorem 1.3
  • Lemma 1.4
  • Corollary 1.5
  • Proposition 2.1
  • Remark 2.2
  • Theorem 2.3
  • proof
  • Definition 3.2
  • ...and 45 more