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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Rational homotopy of the space of self-maps of complexes with finitely many homotopy groups


Author: Samuel B. Smith
Journal: Trans. Amer. Math. Soc. 342 (1994), 895-915
MSC: Primary 55P62; Secondary 55P15, 55P60, 55S37, 55S45
MathSciNet review: 1225575
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Abstract: For simply connected CW complexes X with finitely many, finitely generated homotopy groups,$ ^{1}$ the path components of the function space $ M(X,X)$ of free self-maps of X are all of the same rational homotopy type if and only if all the k-invariants of X are of finite order. In case X is rationally a two-stage Postnikov system the space $ {M_0}(X,X)$ of inessential self-maps of X has the structure of rational H-space if and only if the k-invariants of X are of finite order.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1994-1225575-6
PII: S 0002-9947(1994)1225575-6
Keywords: Function spaces, minimal model, Postnikov tower, rational homotopy equivalence, Hirsch lemma
Article copyright: © Copyright 1994 American Mathematical Society