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Handles, Semihandles, and Destabilization of Isotopies

Published online by Cambridge University Press:  20 November 2018

Dallas E. Webster
Dallas E. Webster*
Affiliation:
State University of New York at Buffalo, Amherst, New York
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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]).

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 27 , Issue 2 , 01 April 1975 , pp. 439 - 445
Copyright
Copyright © Canadian Mathematical Society 1975

References

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