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

Ho, Chung Wu

doi:10.1090/S0002-9947-1973-99929-3

On certain homotopy properties of some spaces of linear and piecewise linear homeomorphisms. II
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by Chung Wu Ho

Trans. Amer. Math. Soc. 181 (1973), 235-243

DOI: https://doi.org/10.1090/S0002-9947-1973-99929-3

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Part I: Trans. Amer. Math. Soc. (1973), 213-233

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.

References

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Homology theory

Chung Wu Ho, On certain homotopy properties of some spaces of linear and piecewise linear homeomorphisms. I, II, Trans. Amer. Math. Soc. 181 (1973), 213–233; ibid. 181 (1973), 235–243. MR 322891, DOI 10.1090/S0002-9947-1973-0322891-3
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