Simplicial bundles and the homology structure of submersions Public Deposited

http://ir.library.oregonstate.edu/concern/graduate_thesis_or_dissertations/2801pk34j

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  • In this dissertation we construct a homology spectral sequence attached to a submersion whose E² term takes values in a certain homology with local coefficients. The motivation for this work is that the spectral sequence provides an effective tool for the conjecture and proof of theorems regarding the global structure of submersions. The spectral sequence is first derived for certain combinatorial objects known as simplicial bundles which at once generalize the notion of fiber bundles (over polyhedra) and simplicial complexes. The spectral sequence of a submersion is then obtained by taking the direct limit of the spectral sequences associated with an approximating system of simplicial bundles.
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