On the topology of nested set complexes
HTML articles powered by AMS MathViewer
- by Eva Maria Feichtner and Irene Müller
- Proc. Amer. Math. Soc. 133 (2005), 999-1006
- DOI: https://doi.org/10.1090/S0002-9939-04-07731-7
- Published electronically: November 19, 2004
- PDF | Request permission
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
- A. Björner, Topological methods, Handbook of combinatorics, Vol. 1, 2, Elsevier Sci. B. V., Amsterdam, 1995, pp. 1819–1872. MR 1373690
- C. De Concini and C. Procesi, Wonderful models of subspace arrangements, Selecta Math. (N.S.) 1 (1995), no. 3, 459–494. MR 1366622, DOI 10.1007/BF01589496
- Eva-Maria Feichtner and Dmitry N. Kozlov, Incidence combinatorics of resolutions, Selecta Math. (N.S.) 10 (2004), no. 1, 37–60. MR 2061222, DOI 10.1007/s00029-004-0298-1
- Eva Maria Feichtner and Sergey Yuzvinsky, Chow rings of toric varieties defined by atomic lattices, Invent. Math. 155 (2004), no. 3, 515–536. MR 2038195, DOI 10.1007/s00222-003-0327-2
- William Fulton and Robert MacPherson, A compactification of configuration spaces, Ann. of Math. (2) 139 (1994), no. 1, 183–225. MR 1259368, DOI 10.2307/2946631
- Daniel Quillen, Homotopy properties of the poset of nontrivial $p$-subgroups of a group, Adv. in Math. 28 (1978), no. 2, 101–128. MR 493916, DOI 10.1016/0001-8708(78)90058-0
- Richard P. Stanley, Enumerative combinatorics. Vol. I, The Wadsworth & Brooks/Cole Mathematics Series, Wadsworth & Brooks/Cole Advanced Books & Software, Monterey, CA, 1986. With a foreword by Gian-Carlo Rota. MR 847717, DOI 10.1007/978-1-4615-9763-6
Bibliographic 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
- 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
- © Copyright 2004 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 133 (2005), 999-1006
- MSC (2000): Primary 06A11; Secondary 05E25, 32S45, 57N80
- DOI: https://doi.org/10.1090/S0002-9939-04-07731-7
- MathSciNet review: 2117200