Algebraic Hopf invariants and rational models for mapping spaces

2016/12/22 by Wierstra, Felix
#Algebraic Topology (math.AT) #FOS: Mathematics

paper · doi:10.48550/arxiv.1612.07762

Abstract

In this paper we will define an invariant mc_∞(f) of maps f:X → Y_ℚ between a finite CW-complex and a rational space Y_ℚ. We prove that this invariant is complete, i.e. mc_∞(f)=mc_∞(g) if an only if f and g are homotopic. We will also construct an L_∞-model for the based mapping space Map_*(X,Y_ℚ) from a C_∞-coalgebra and an L_∞-algebra.

Related

• L_infty rational homotopy of mapping spaces
• Lie coalgebras and rational homotopy theory II: Hopf invariants
• Rational formality of mapping spaces
• Rational homotopy type of mapping spaces via cohomology algebras
• On a notion of maps between orbifolds, II. homotopy and CW-complex