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Transactions of the American Mathematical Society

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

 
 

 

The group of $PL$-homeomorphisms of a compact $PL$-manifold is an $1^{f}_{2}$-manifold


Authors: James Keesling and David C. Wilson
Journal: Trans. Amer. Math. Soc. 193 (1974), 249-256
MSC: Primary 57E05; Secondary 57A20
DOI: https://doi.org/10.1090/S0002-9947-1974-0368046-9
MathSciNet review: 0368046
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Abstract: In this paper it is shown that if $M$ is a compact PL-manifold and ${H_{PL}}(M)$ is the group of PL-homeomorphisms of $M$ onto itself, then ${H_{PL}}(M)$ is an $l_2^f$-manifold. Here ${l_2}$ is the Hilbert space of all real-valued square-summable sequences and $l_2^f = \{ ({x_i}) \in {l_2}:{x_i} = 0$ for almost all $i$.


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Keywords: PL-manifold, PL-homeomorphism, <IMG WIDTH="23" HEIGHT="49" ALIGN="MIDDLE" BORDER="0" SRC="images/img1.gif" ALT="$l_2^f$">-manifold
Article copyright: © Copyright 1974 American Mathematical Society