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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 
 

 

Modèle minimal équivariant et formalité


Author: Thierry Lambre
Journal: Trans. Amer. Math. Soc. 327 (1991), 621-639
MSC: Primary 55P91; Secondary 55P62
DOI: https://doi.org/10.1090/S0002-9947-1991-1049613-6
MathSciNet review: 1049613
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Abstract: We study the rational equivariant homotopy type of a topological space $ X$ equipped with an action of the group of integers modulo $ n$.

For $ n= {p^k}$ ($ p$ prime, $ k$ a positive integer), we build an algebraic model which gives the rational equivariant homotopy type of $ X$. The homotopical fixed-point set appears in the construction of a model of the fixed-points set. In general, this model is different from $ {\text{G}}$. Triantafillou's model $ [{\text{T1}}]$.

For $ n= p$ ($ p$ prime), we then give a notion of equivariant formality. We prove that this notion is equivalent to the formalizability of the inclusion of fixed-points set $ i:{X^{{\mathbb{Z}_p}}} \to X$. Examples and counterexamples of $ {\mathbb{Z}_p}$-formal spaces are given.


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DOI: https://doi.org/10.1090/S0002-9947-1991-1049613-6
Keywords: $ G$-space, differential algebra, minimal model
Article copyright: © Copyright 1991 American Mathematical Society

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