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Cobordism span of a manifold and elliptic genera. (English) Zbl 0659.57017

The power of two that divides the twisted signature is an obstruction to vector fields on a 4k-dimensional manifold. The universal elliptic genus is used to compute this obstruction.
Reviewer: M.Bendersky

MSC:

57R25 Vector fields, frame fields in differential topology
57R20 Characteristic classes and numbers in differential topology
57R75 \(\mathrm{O}\)- and \(\mathrm{SO}\)-cobordism
58J26 Elliptic genera
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References:

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