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Cobordism Obstructions to Vector Fields and a Generalization of Lin's Theorem

by Anne Marie Svane
PhD Dissertations | October 2011
Atiyah and Dupont have studied the existence of linearly independent vector fields on manifolds by means of K-theory. They obtained the complete conditions for up to three independent vector fields. In the thesis, we try to copy their approach using certain spectra related to cobordism theory. We compute the homotopy groups of these spectra in low dimensions using the Adams spectral sequence. From this we obtain conditions for the top obstruction to be an invariant, and in certain cases, we identify this. We also consider an inverse limit system formed by these spectra and prove that it generalizes Lin's inverse system in compact cases, while it behaves completely differently in the universal case.
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Thesis advisor: Marcel Bökstedt and Johan Dupont