Daniel Quillen, the father of abstract homotopy theory

2013 ◽  
Vol 11 (3) ◽  
pp. 479-491
Author(s):  
Jean-Claude Thomas ◽  
Micheline Vigué-Poirrier
Keyword(s):  
Homotopy Theory ◽  
Short Paper ◽  
Rational Homotopy Theory ◽  
Rational Homotopy ◽  
Abstract Homotopy Theory

AbstractIn this short paper we try to describe the fundamental contribution of Quillenin the development of abstract homotopy theory and we explain how he uses this theory to lay the foundations of rational homotopy theory.

On equivariant disconnected rational homotopy theory

2010 ◽  
Vol 17 (2) ◽  
pp. 229-240
Author(s):  
Marek Golasiński
Keyword(s):  
Homotopy Theory ◽  
Weak Equivalence ◽  
Rational Homotopy Theory ◽  
Rational Homotopy ◽  
Hamiltonian Group ◽  
Simplicial Set ◽  
De Rham

Abstract An equivariant disconnected Sullivan–de Rham equivalence is developed using Kan's result on diagram categories. Given a finite Hamiltonian group G, let X be a G-simplicial set. It is shown that the associated system of algebras indexed by the category 𝒪(G) of a canonical orbit can be “approximated” (up to a weak equivalence) by such a system ℳ X with the properties required by nonequivariant minimal algebras.

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