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On the topology of nested set complexes

Eva Maria Feichtner·Irene Mueller
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Abstract

Nested set complexes appear as the combinatorial core of De Concini-Procesi arrangement models. We show that nested set complexes are homotopy equivalent to the order complexes of the underlying meet-semilattices without their minimal elements. For atomic semilattices, we consider the realization of nested set complexes by simplicial fans as proposed in math.AG/0305142 by the first author and S. Yuzvinsky. We show that in this case the nested set complexes in fact are homeomorphic to the mentioned order complexes.

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Eva Maria Feichtner, Irene Mueller. 2003-11-25. On the topology of nested set complexes. https://arxiv.org/abs/math/0311430

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