Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
|
   
Available in electronic format
Available in print format 		Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(e) ISSN 0002-9939(p)

     

On the topology of nested set complexes

Author(s): Eva Maria Feichtner; Irene Müller
Journal: Proc. Amer. Math. Soc. 133 (2005), 999-1006.
MSC (2000): Primary 06A11; Secondary 05E25, 32S45, 57N80
Posted: November 19, 2004
MathSciNet review: 2117200
Retrieve article in: PDF
This article is available free of charge

Abstract | References | Similar articles | Additional information

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.

References:

1.
A. Björner: Topological methods; in: Handbook of Combinatorics (R. Graham, M. Grötschel, L. Lovász, eds); North-Holland, Amsterdam 1995, pp. 1819-1872. MR 1373690 (96m:52012)

2.
C. De Concini, C. Procesi: Wonderful models of subspace arrangements; Selecta Math. (N.S.) 1 (1995), 459-494. MR 1366622 (97k:14013)

3.
E.M. Feichtner, D.N. Kozlov: Incidence combinatorics of resolutions; Selecta Math. (N.S.) 10 (2004), 37-60. MR 2061222

4.
E.M. Feichtner, S. Yuzvinsky: Chow rings of toric varieties defined by atomic lattices; Invent. Math. 155 (2004), 515-536. MR 2038195

5.
W. Fulton, R. MacPherson: A compactification of configuration spaces; Ann. of Math. 139 (1994), 183-225. MR 1259368 (95j:14002)

6.
D. Quillen: Homotopy properties of the poset of non-trivial $p$-subgroups of a group; Advances in Math. 21 (1978), 101-128. MR 0493916 (80k:20049)

7.
R. Stanley: Enumerative combinatorics, Vol. I, Wadsworth & Brooks/Cole, Monterey, Calif., 1986. MR 0847717 (87j:05003)

Similar Articles:

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 06A11, 05E25, 32S45, 57N80

Retrieve articles in all Journals with MSC (2000): 06A11, 05E25, 32S45, 57N80

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: 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
Posted: November 19, 2004
Additional Notes: The second author was supported by ETH research grant TH-10/02-3.
Communicated by: Paul Goerss
Copyright of article: Copyright 2004, American Mathematical Society




AMS and Social Media LinkedIn Facebook Podcasts Twitter YouTube RSS Feeds Blogs Wikipedia