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The "polyhedral product functor" produces a space from a simplicial complex L and a collection of pairs of spaces, {(A(i),B(i))}, where i ranges over the vertex set of L. We give necessary and sufficient conditions for the resulting space to be aspherical. There are two similar constructions, each of which starts with a space X and a collection of subspaces, {X_i} and then produces a new space. We give conditions for the results of these constructions to be aspherical. All three techniques can be used to produce examples of closed aspherical manifolds. Abstract for Corrigenda: This note concerns two refinements to the earlier work by the first author. First, when L is infinite, the definition of polyhedral product needs clarification. Second, the earlier paper omitted some subtle parts of the necessary and sufficient conditions for polyhedral products to be aspherical. Correct versions of these necessary and sufficient conditions are given in the present paper.Comment: Includes some typographical changes from the first version and a 7 page corrigenda written with Peter Kropholler and attached as a separate documen

Topics:
Mathematics - Geometric Topology, Mathematics - Group Theory, 20E40, 20F65, 57M07, 57M10 (Primary), 20F36, 20E42, 20F55
(Secondary)

Year: 2015

OAI identifier:
oai:arXiv.org:1102.4670

Provided by:
arXiv.org e-Print Archive

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