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Compact Hilbert cube manifolds and the invariance of Whitehead torsion. (English) Zbl 0251.57004


MSC:

57N20 Topology of infinite-dimensional manifolds
57Q10 Simple homotopy type, Whitehead torsion, Reidemeister-Franz torsion, etc.
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[1] R. D. Anderson, On topological infinite deficiency, Michigan Math. J. 14 (1967), 365 – 383. · Zbl 0148.37202
[2] R. D. Anderson and T. A. Chapman, Extending homeomorphisms to Hilbert cube manifolds, Pacific J. Math. 38 (1971), 281 – 293. · Zbl 0227.57004
[3] Karol Borsuk, Theory of retracts, Monografie Matematyczne, Tom 44, Państwowe Wydawnictwo Naukowe, Warsaw, 1967. · Zbl 0153.52905
[4] T. A. Chapman, Hilbert cube manifolds, Bull. Amer. Math. Soc. 76 (1970), 1326 – 1330. · Zbl 0205.53601
[5] T. A. Chapman, On the structure of Hilbert cube manifolds, Compositio Math. 24 (1972), 329 – 353. · Zbl 0246.57005
[6] T. A. Chapman, Surgery and handle straightening in Hilbert cube manifolds, Pacific J. Math. 45 (1973), 59 – 79. · Zbl 0267.57006
[7] T. A. Chapman, Topological invariance of Whitehead torsion, Amer. J. Math. (submitted). · Zbl 0358.57004
[8] R. C. Kirby and L. C. Siebenmann, For manifolds the Hauptvermutung and the triangulation conjecture are false, Notices Amer. Math. Soc. 16 (1969), 695. Abstract #69T-G80. · Zbl 0189.54701
[9] R. C. Kirby and L. C. Siebenmann, On the triangulation of manifolds and the Hauptvermutung, Bull. Amer. Math. Soc. 75 (1969), 742 – 749. · Zbl 0189.54701
[10] A. Lundell and S. Weingram, The topology of CW-complexes, Van Nostrand Reinhold, New York, 1969. · Zbl 0207.21704
[11] J. Milnor, Whitehead torsion, Bull. Amer. Math. Soc. 72 (1966), 358 – 426. · Zbl 0147.23104
[12] L. C. Siebenmann, On the homotopy type of compact topological manifolds, Bull. Amer. Math. Soc. 74 (1968), 738 – 742. · Zbl 0165.56703
[13] James E. West, Mapping cylinders of Hilbert cube factors, General Topology and Appl. 1 (1971), no. 2, 111 – 125. · Zbl 0224.57004
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