Journal of the Mathematical Society of Japan

L∞ models of based mapping spaces

Urtzi BUIJS, Yves FÉLIX, and Aniceto MURILLO

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Abstract

In this paper, for any pointed map f: X → Y between finite type nilpotent CW-complexes, we obtain L∞ and Lie models of mapf*(X,Y), the pointed space of based maps homotopic to f, in terms of Lie algebras constructed from the Quillen models of X and Y. The main advantage of our approach is to allow X to be an infinite dimensional CW-complex, in which case mapf*(X,Y) has no longer the homotopy type of a finite type CW-complex.

Article information

Source
J. Math. Soc. Japan, Volume 63, Number 2 (2011), 503-524.

Dates
First available in Project Euclid: 25 April 2011

Permanent link to this document
https://projecteuclid.org/euclid.jmsj/1303737796

Digital Object Identifier
doi:10.2969/jmsj/06320503

Mathematical Reviews number (MathSciNet)
MR2793109

Zentralblatt MATH identifier
1252.55006

Subjects
Primary: 55P62: Rational homotopy theory 54C35: Function spaces [See also 46Exx, 58D15]

Keywords
mapping space L_∞ algebra Quillen model rational homotopy theory

Citation

BUIJS, Urtzi; FÉLIX, Yves; MURILLO, Aniceto. L ∞ models of based mapping spaces. J. Math. Soc. Japan 63 (2011), no. 2, 503--524. doi:10.2969/jmsj/06320503. https://projecteuclid.org/euclid.jmsj/1303737796


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