Geodesic
Handles, Semihandles, and Destabilization of Isotopies
Canadian journal of mathematics, Tome 27 (1975) no. 2, pp. 439-445

Voir la notice de l'article provenant de la source Cambridge University Press

Kirby and Siebenmann showed that handles of index other than 3 can be straightened, and then went on to prove an abundance of immensely important results such as triangulation theorems, Hauptvermutungen, and classification and structure theorems. (See [7; 6; 2; 3; 8; 4; 5].) Their pr∞fs relied on some nonsimply connected surgery techniques and computations due to Wall, Hsiang, and Shaneson [10; 11; 12; 1], which at the time seemed so difficult as to be practically inaccessible to the large number of mathematicians interested in the consequences. The main result presented here, viz., that a stably straightened handle can be straightened, was obtained by the author some time ago in an attempt to prove the stable homeomorphism theorem without the assistance of Wall, Hsiang and Shaneson (cf. [13]). 
Webster, Dallas E. Handles, Semihandles, and Destabilization of Isotopies. Canadian journal of mathematics, Tome 27 (1975) no. 2, pp. 439-445. doi: 10.4153/CJM-1975-052-3
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[1] 1. Hsiang, W. C. and Shaneson, J. L., Fake tori, the annulus conjecture, and the conjectures of Kirby, Proc. Nat. Acad. Sci. U.S.A. 62 (1969), 687–691. Google Scholar

[2] 2. Kirby, R. C., Lectures on triangulations of manifolds, Mimeographed lecture notes, U.C.L.A., 1969. Google Scholar

[3] 3. Kirby, R. C., Stable homeomorphisms and the annulus conjecture, Ann. of Math. 89 (1969), 575–582. Google Scholar

[4] 4. Kirby, R. C. and Siebenmann, L. C., Classification of sm∞th and piecewise-linear manifold structures (to appear). Google Scholar

[5] 5. Kirby, R. C. and Siebenmann, L. C., Deformations of sm∞th and piecewise linear manifold structures (to appear). Google Scholar

[6] 6. Kirby, R. C. and Siebenmann, L. C., For manifolds the Hauptvermutung and the triangulation conjecture are false, Notices Amer. Math. Soc. 16 (1969), p. 695. Google Scholar

[7] 7. Kirby, R. C. and Siebenmann, L. C., On the triangulation of manifolds and the Hauptvermutung, Bull. Amer. Math. Soc. 75 (1969), 742–749. Google Scholar

[8] 8. Kirby, R. C. and Siebenmann, L. C., Some theorems on topological manifolds, Manifolds-Amsterdam 1970, Lecture Notes in Mathematics, No. 197 (Springer-Verlag, New York, 1971). Google Scholar

[9] 9. Stallings, J., Lectures on polyhedral topology (Tata Institute of Fundamental Research, Bombay, 1967). Google Scholar

[10] 10. Wall, C. T. C., On homotopy tori and the annulus conjecture, Bull. Lond. Math. Soc. 1 (1969), 95–97. Google Scholar

[11] 11. Wall, C. T. C., Surgery on compact manifolds (Academic Press, New York, 1970). Google Scholar

[12] 12. Wall, C. T. C. and Hsiang, W. C., On homotopy tori, II, Bull. Lond. Math. Soc. 1 (1969), 341–342. Google Scholar

[13] 13. Webster, D. E., Alternate methods in handle-straightening theory, Ph.D. Thesis, University of Wisconsin, 1970. Google Scholar

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