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arXiv:1206.3368 [math.AT]AbstractReferencesReviewsResources

A note on the homotopy type of the Alexander dual

Elias Gabriel Minian, Jorge Tomas Rodriguez

Published 2012-06-15Version 1

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.

Comments: 6 pages
Categories: math.AT, math.CO
Subjects: 55U05, 55P15, 57Q05, 57Q10, 55M05, 06A06
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