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arXiv · 1711.08179

Reducibility of low dimensional Poincar\'e duality spaces

Markus Land
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Abstract

We discuss Poincar\'e duality complexes X and the question whether or not their Spivak normal fibration admits a reduction to a vector bundle in the case where the dimension of X is at most 4. We show that in dimensions less than 4 such a reduction always exists, and in dimension 4 such a reduction exists provided X is orientable. In the non-orientable case there are counterexamples to reducibility by Hambleton--Milgram.

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Markus Land. 2017-11-22. Reducibility of low dimensional Poincar\'e duality spaces. https://arxiv.org/abs/1711.08179

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