Homology, Homotopy and Applications

Volume 6 (2004)

Number 1

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

Pages: 341 – 350

DOI: http://dx.doi.org/10.4310/HHA.2004.v6.n1.a18


Yasusuke Kotani (Department of Mathematics, Faculty of Science, Kochi University, Kochi, Japan)


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 $q \ge \dim{X}$, 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.


rational cohomology, function spaces, free commutative graded algebras, formal spaces

2010 Mathematics Subject Classification

Primary 55P62. Secondary 54C40.

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