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A note on the homotopy type of PL2

Published online by Cambridge University Press:  24 October 2008

G. P. Scott
G. P. Scott
Affiliation:
University of Liverpool
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Extract

Let O2 denote the group of isometrics of the plane R2 fixing the origin and let PL2 denote the space of piecewise-linear (PL) homeomorphisms of R2 fixing the origin. Akiba has proved that PL2 is homotopy equivalent to O2(1). The purpose of this note is to point out that this result can be proved by the methods of the author in (4). A complete proof of this result using these methods appeared in the author's Ph.D. thesis(5).

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 69 , Issue 2 , March 1971 , pp. 257 - 258
Copyright
Copyright © Cambridge Philosophical Society 1971

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References

REFERENCES

(1)Akiba, T.On the homotopy type of PL 2. J. Fac. Sci. Univ. Tokyo Sect. I, 14 (1967), 197–204.Google Scholar
(2)Hirsch, M. W.On non-linear cell bundles. Ann. of Math. 84 (1966), 373–385.Google Scholar
(3)Kan, D. M.A combinatorial definition of homotopy groups. Ann. of Math. 67 (1958), 282–312.CrossRefGoogle Scholar
(4)Scott, G. P.The space of homeomorphisms of a 2-manifold. Topology 9 (1970), 97–109.Google Scholar
(5)Scott, G. P. Ph.D. thesis, University of Warwick, 1968.Google Scholar