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arXiv · 1206.3368

A note on the homotopy type of the Alexander dual

Elias Gabriel Minian·Jorge Tomas Rodriguez
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Abstract

We investigate the homotopy type of the Alexander dual of a simplicial complex. In general the homotopy type of K does not determine the homotopy type of its dual K*. Moreover, one can construct for each finitely presented group G, a simply connected simplicial complex K with fundamental group isomorphic to G. We study sufficient conditions on K for K* to have the homotopy type of a sphere. We also extend the simplicial Alexander duality to the context of reduced lattices.

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Elias Gabriel Minian, Jorge Tomas Rodriguez. 2012-06-15. A note on the homotopy type of the Alexander dual. https://arxiv.org/abs/1206.3368

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