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Non-simply connected H-spaces with finiteness conditions

Published online by Cambridge University Press:  18 May 2001

CARLES BROTO ,
JUAN A. CRESPO  and
LAIA SAUMELL
CARLES BROTO
Affiliation:
Departament de Matemàtiques, Universitat Autònoma de Barcelona, E-08193 Bellaterra, Spain. e-mail: broto@mat.uab.es
JUAN A. CRESPO
Affiliation:
Centre de Recerca Matemàtica, Institut d'Estudis Catalans, E-08913 Bellaterra, Spain. e-mail: chiqui@crm.es
LAIA SAUMELL
Affiliation:
Departament de Matemàtiques, Universitat Autònoma de Barcelona, E-08193 Bellaterra, Spain. e-mail: laia@mat.uab.es
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Abstract

This article is concerned with homotopy properties of H-spaces X that are reflected in the module of indecomposables QH*(X; [ ]p). It is shown that mod p H-spaces X of finite type with finite transcendence degree mod p cohomology and locally finite QH*(X; [ ]p) are Bℤ/p-null spaces, Eilenberg–MacLane spaces K(ℤˆp, 2), K(ℤ/pr, 1), and extensions of those. If we restrict attention to H-spaces with noetherian mod p cohomology algebra, then we are left with finite mod p H-spaces and Eilenberg–MacLane spaces.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 130 , Issue 3 , May 2001 , pp. 475 - 488
Copyright
2001 Cambridge Philosophical Society

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