A generalization of a result of Dong and Santos-Sturmfels on the Alexander dual of spheres and balls

Nicolas Ariel Capitelli; Elias Gabriel Minian

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arXiv · 1403.1291

A generalization of a result of Dong and Santos-Sturmfels on the Alexander dual of spheres and balls

Nicolas Ariel Capitelli·Elias Gabriel Minian

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Abstract

We prove a generalization of a result by Dong and Santos-Sturmfels about the homotopy type of the Alexander dual of balls and spheres. Our results involve NH-manifolds, which were recently introduced as the non-homogeneous (or non-pure) counterpart of classical polyhedral manifolds. We show that the Alexander dual of an NH-ball is contractible and the Alexander dual of an NH-sphere is homotopy equivalent to a sphere. We also prove that NH-balls and NH-spheres arise naturally as the double duals of standard balls and spheres.

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Nicolas Ariel Capitelli, Elias Gabriel Minian. 2014-03-05. A generalization of a result of Dong and Santos-Sturmfels on the Alexander dual of spheres and balls. https://arxiv.org/abs/1403.1291

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