Browsing by Author "Cherenack, Paul F"

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    The right exactness of the smooth right Puppe sequence
    (1996) Dugmore, Brett; Cherenack, Paul F
    It was our aim, in this thesis, to give a proof that the smooth right Puppe sequence exists and is right exact, following the methods used by Whitehead in (30], and where he shows that the usual continuous right Puppe sequence exists and is right exact. We have only partially been able meet this aim. We have attempted to follow the general approach of Steenrod [27], where he defines neighbourhood deformation retracts, but there are some difficulties involved in the theory of smooth neighbourhood deformation retracts that have made it necessary for us to assume the existence of a 'suitable' smooth structure on products such as I x X x Y, where (X, A), and (Y, B) are smooth neighbourhood deformation retracts, such that the product, defined as (X x Y, Ax Y U X x A), is an SNDR pair under this 'suitable' product structure. This enables us to develop the theory of smooth neighbourhood deformation retracts in a similar way to the theory of continuous neighbourhood deformation retracts.