A note on the homotopy type of the Alexander dual
Algebraic Topology
2012-06-18 v1 Combinatorics
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.
Cite
@article{arxiv.1206.3368,
title = {A note on the homotopy type of the Alexander dual},
author = {Elias Gabriel Minian and Jorge Tomas Rodriguez},
journal= {arXiv preprint arXiv:1206.3368},
year = {2012}
}
Comments
6 pages