content_image/327632.jpg content_image/327631.jpg
specified in Equations (2.12) and (2.13) to get 

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To gain a better understanding of how the two sets of bounds compare, we compute these bounds explicitly for the case of a 2-current in a regular tetrahedral complex (thus, p = 3 and d = 2). Notice that this instance is close to a best case for Sullivan’s bounds, as less regular complexes affect them more severely. With this point in mind, we present in Table 2.1 our bounds and Sullivan’s bounds on both a regular tetrahedral complex and one on which we stretch the regular tetrahedra by a factor of 10 in a direction normal to one of their faces (i.e., turn them into skinny, spike-like simplices). 

<img src='content_image/327631.jpg'>

