## Homology, Homotopy and Applications

### Note on the rational cohomology of the function space of based maps

Yasusuke Kotani

#### Abstract

In this paper, for a formal, path connected, finite-dimensional CW-complex $X$ of finite type and a $q$-connected space $Y$ of finite type with $q \geq \rm{dim} X$, we determine the necessary and sufficient condition for the rational cohomology algebra $H^*(\mathcal{F}_*(X,Y);\mathbb{Q})$ of the function space $\mathcal{F}_*(X,Y)$ of based maps to be free.

#### Article information

Source
Homology Homotopy Appl., Volume 6, Number 1 (2004), 341-350.

Dates
First available in Project Euclid: 13 February 2006

https://projecteuclid.org/euclid.hha/1139839557

Mathematical Reviews number (MathSciNet)
MR2084591

Zentralblatt MATH identifier
1065.55005

Subjects
Primary: 55P62: Rational homotopy theory

#### Citation

Kotani, Yasusuke. Note on the rational cohomology of the function space of based maps. Homology Homotopy Appl. 6 (2004), no. 1, 341--350. https://projecteuclid.org/euclid.hha/1139839557