The relationship between the boundedly controlled K1 and Whitehead groups |
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Authors: | Douglas R Anderson |
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Institution: | (1) Department of Mathematics, Syracuse University, 13244, NY, USA |
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Abstract: | Let Z be a boundedness control space and p: X Z be a continuous map. The boundedly controlled Whitehead group Wh
bc
(X, p) is defined to be a quotient of the boundedly controlled K
1-group K
1
bc
(X, p) by a certain subgroup whose generators are explicitly given. In general, little is known about this subgroup and it is even possible that it vanishes; i.e. that the boundedly controlled K
1 and Whitehead groups are identical. This paper examines the structure of this subgroup in the case when p is the open cone on a PL map between compact polyhedra. As a byproduct, it calculates Wh
bc
(X, p) in some of these cases.Partially supported by the NSF under grant number DMS-8803149. |
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Keywords: | Boundedly controlled K
1 boundedly controlled Whitehead group boundedly controlled topology controlled topology geometric modules |
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