Non-simplicially collapsible triangulations of In

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Abstract
Given any triangulation of a topological n-cell, In, there is an integer k such that the kth barycentric subdivision of the triangulation is simplicially collapsible (3). In the following, we show that given any integer k, we can construct a triangulation of an n-cell, n > 2, whose kth barycentric subdivision is not simplicially collapsible.