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Transactions of the American Mathematical Society

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On certain homotopy properties of some spaces of linear and piecewise linear homeomorphisms. II

Author: Chung Wu Ho
Journal: Trans. Amer. Math. Soc. 181 (1973), 235-243
MSC: Primary 57E05; Secondary 57C05
Part I: Trans. Amer. Math. Soc. (1973), 213-233
MathSciNet review: 0322891
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Abstract: In his study of the smoothings of p. l. manifolds, R. Thom considered the homotopy groups of a certain space $ {L_n}$ of p.l. homeomorphisms on an $ n$-simplex. N. H. Kuiper showed in 1965 that the higher homotopy groups of $ {L_n}$ were in general nontrivial. The main result in this paper is that $ {\pi _0}({L_2}) = {\pi _1}({L_2}) = 0$.

The proof of this result is based on a theorem of S. S. Cairns in 1944 on the deformation of rectilinear complexes in $ {R^2}$ and a theorem established in Part I of this paper.

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Keywords: Simplicial subdivision, proper subdivision, rectilinear cell complex, inductive limit, the space of linear isomorphisms on a complex
Article copyright: © Copyright 1973 American Mathematical Society