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Sectional category à la Quillen

Urtzi Buijs, José Carrasquel

Abstract

In this note we give a characterization of the sectional category of a map between rational spaces in terms of its Koszul-Quillen model.

Sectional category à la Quillen

Abstract

In this note we give a characterization of the sectional category of a map between rational spaces in terms of its Koszul-Quillen model.
Paper Structure (2 sections, 6 theorems, 12 equations)

This paper contains 2 sections, 6 theorems, 12 equations.

Table of Contents

  1. Preliminaries
  2. Proof of Theorem

Key Result

Theorem 1

Let $\varphi\colon(\mathbb{L} (V),\partial)\rightarrowtail (\mathbb{L} (V\oplus W), \partial)$ be the Koszul-Quillen model of certain continuous map $f\colon X\to Y$ between simply connected rational spaces. Then the sectional category of $f$ is the smallest $n$ for which there exists a dgl map such that, for all $a\in V\oplus W$, $\alpha(a)=a_1+\cdots +a_{n+1}+\xi$ with Here $U^{n+1}$ denotes t

Theorems & Definitions (10)

  • Theorem
  • Proposition 1.1
  • Proposition 1.2
  • Proposition 1.3
  • Lemma 1.4
  • proof
  • Lemma 1.5
  • proof
  • proof : Proof of Proposition \ref{['prop:ModelFor2']}
  • Remark 1.6