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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



The free topological group on a simply connected space

Authors: J. P. L. Hardy and Sidney A. Morris
Journal: Proc. Amer. Math. Soc. 55 (1976), 155-159
MSC: Primary 57F20; Secondary 22A05
MathSciNet review: 0424993
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Abstract: It is shown that the free $ k$-group on a simply connected locally equiconnected space is simply connected. This result is then used to verify, for a large class of groups, the conjecture of Ordman that $ {\pi _1}(G{\ast}H) = {\pi _1}(G) \times {\pi _1}(H)$, where $ G{\ast}H$ is the free product of $ G$ and $ H$.

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Keywords: Free topological group, $ k$-group, simply connected, free product of $ k$-groups, locally equiconnected, cofibration, van Kampen theorem, fundamental groupoid
Article copyright: © Copyright 1976 American Mathematical Society