Algebraic Hopf invariants and rational models for mapping spaces

Abstract

In this paper we will define an invariant $m{c}_{\infty }(f)$ of maps $f:X\to Y_{\mathbb{Q}}$ between a finite CW-complex and a rational space $Y_{\mathbb{Q}}$. We prove that this invariant is complete, i.e. $m{c}_{\infty }(f)=m{c}_{\infty }(g)$ if an only if $f$ and $g$ are homotopic. We will also construct an $L_{\infty }$-model for the based mapping space $Ma{p}_{\ast }(X,Y_{\mathbb{Q}})$ from a $C_{\infty }$-coalgebra and an $L_{\infty }$-algebra.

arXiv commentImproved certain sections of the paper, corrected some errors. 18 pages