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Buoncristiano, Sandro (1973) Coefficients in bordism. PhD thesis, University of Warwick.

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Official URL: http://webcat.warwick.ac.uk/record=b1736251~S1
Abstract
In this paper is given a treatment of coefficients for a vast class of (co)bordism theories of manifolds with singularities. If h() is one of these theories and G is an abelian group we introduce coefficients G into h in such a way that
(a) h(; G) is a functor on the category of all abelian groups;
(b) the universalcoefficient sequence is natural on the category of all abelian groups. Consequently, by [5], it is pure
and hence, by algebra, it splits for a vast class of abelian groups, including all groups of finite type.
(c) If G is an Rmodule, R any commutative ring with unit, h(; G) inherits an Rmodule and h(point; R)module structure in a natural way. It follows from Dold [3] that there is a generalized universalcoefficient sequence consisting of a spectral sequence running Torp(hq(;R),G)=>h(; G).
(d) When h() = H(;Z) singular (co)homology with integer coefficients, the definition coincides with the usual one given by means of chain complexes.
(e) The method works to introduce local coefficients in the cohomology theory h*() ; i.e. if F is any sheaf of modules over a compact polyhedron X, then h*(X; F) is defined and it is a functor on sheaves.
(f) If F/x is a 'nice' sheaf (in the sense of III.3), there is a spectral sequence running
Hp(X; hqF) => h*(X; F) (*)
where hqF is the graded sheaf obtained from F by applying the functor hq(point; ) and H is singular cohomology. When F is constant, (*) reduces to the usual type. A comparison theorem is deduced from (*) by means of the Mapping Theorem between spectral sequences.
Item Type:  Thesis (PhD)  

Subjects:  Q Science > QA Mathematics  
Library of Congress Subject Headings (LCSH):  Manifolds (Mathematics), Singularities (Mathematics)  
Official Date:  1973  
Dates: 


Institution:  University of Warwick  
Theses Department:  Mathematics Institute  
Thesis Type:  PhD  
Publication Status:  Unpublished  
Supervisor(s)/Advisor:  Rourke, C. P. (Colin Patrick), 1943  
Sponsors:  Consiglio nazionale delle ricerche (Italy)  
Extent:  iv, 76 leaves  
Language:  eng 
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