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h-COBORDISMS AND MAPPING CYLINDER OBSTRUCTIONS

Part of: PL-topology Topological manifolds

Published online by Cambridge University Press:  01 April 2009

BOGDAN VAJIAC
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: bvajiac@saintmarys.edu)
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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.

Keywords

stratified spacecobordismmapping cylinder obstruction

MSC classification

Secondary: 57Q10: Simple homotopy type, Whitehead torsion, Reidemeister-Franz torsion, etc. 57Q40: Regular neighborhoods 57N40: Neighborhoods of submanifolds 57N80: Stratifications
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 86 , Issue 2 , April 2009 , pp. 249 - 278
Copyright
Copyright © Australian Mathematical Society 2009

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