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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

On the topology of nested set complexes


Authors: Eva Maria Feichtner and Irene Müller
Journal: Proc. Amer. Math. Soc. 133 (2005), 999-1006
MSC (2000): Primary 06A11; Secondary 05E25, 32S45, 57N80
Published electronically: November 19, 2004
MathSciNet review: 2117200
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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 proposed by the first author and Yuzvinsky and we strengthen our previous result showing that in this case nested set complexes in fact are homeomorphic to the mentioned order complexes.


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Additional Information

Eva Maria Feichtner
Affiliation: Department of Mathematics, ETH Zurich, 8092 Zurich, Switzerland
Email: feichtne@math.ethz.ch

Irene Müller
Affiliation: Department of Mathematics, ETH Zurich, 8092 Zurich, Switzerland
Email: irene@math.ethz.ch

DOI: http://dx.doi.org/10.1090/S0002-9939-04-07731-7
PII: S 0002-9939(04)07731-7
Keywords: Nested set complexes, order complexes, combinatorial stratifications
Received by editor(s): December 12, 2003
Published electronically: November 19, 2004
Additional Notes: The second author was supported by ETH research grant TH-10/02-3.
Communicated by: Paul Goerss
Article copyright: © Copyright 2004 American Mathematical Society



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