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On the space of piecewise linear homeomorphisms of a manifold


Authors: Ross Geoghegan and William E. Haver
Journal: Proc. Amer. Math. Soc. 55 (1976), 145-151
MSC: Primary 57E05; Secondary 57C99
DOI: https://doi.org/10.1090/S0002-9939-1976-0402785-3
MathSciNet review: 0402785
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Abstract: Let $ {M^n}$ be a compact PL manifold, $ n \ne 4$; if $ n = 5$, suppose $ \partial M$ is empty. Let $ H(M)$ be the space of homeomorphisms on $ M$ and $ {H^{\ast}}(M)$ the elements of $ H(M)$ which are isotopic to PL homeomorphisms. It is shown that the space of PL homeomorphisms, $ PLH(M)$, has the finite dimensional compact absorption property in $ {H^{\ast}}(M)$ and hence that $ ({H^{\ast}}(M),PLH(M))$ is an $ ({l_2},l_2^f)$-manifold pair if and only if $ H(M)$ is an $ {l_2}$-manifold. In particular, if $ {M^2}$ is a $ 2$-manifold, $ (H({M^2}),PLH({M^2}))$ is an $ ({l_2},l_2^f)$-manifold pair.


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DOI: https://doi.org/10.1090/S0002-9939-1976-0402785-3
Article copyright: © Copyright 1976 American Mathematical Society

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