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h-COBORDISMS AND MAPPING CYLINDER OBSTRUCTIONS

Published online by Cambridge University Press:  01 April 2009

BOGDAN VAJIAC*
Affiliation:
Department of Mathematics, Indiana University Northwest, 3400 Broadway, Gary IN 46408, USA Current address: Department of Mathematics, Saint Mary’s College, Notre Dame, IN 46556, USA (email: [email protected])
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Abstract

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In this paper we prove a realizability theorem for Quinn’s mapping cylinder obstructions for stratified spaces. We prove a continuously controlled version of the s-cobordism theorem which we further use to prove the relation between the torsion of an h-cobordism and the mapping cylinder obstructions. This states that the image of the torsion of an h-cobordism is the mapping cylinder obstruction of the lower stratum of one end of the h-cobordism in the top filtration. These results are further used to prove a theorem about the realizability of end obstructions.

Type
Research Article
Copyright
Copyright © Australian Mathematical Society 2009

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