Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

Formality of Pascal arrangements


Authors: Matthew Miller and Max Wakefield
Journal: Proc. Amer. Math. Soc. 139 (2011), 4461-4466
MSC (2010): Primary 52C35; Secondary 55R80
DOI: https://doi.org/10.1090/S0002-9939-2011-11009-8
Published electronically: April 5, 2011
MathSciNet review: 2823091
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: In this paper we construct a family of subspace arrangements whose intersection lattices have the shape of Pascal's triangle. We prove that even though the intersection lattices are not geometric, the complex complement of the arrangements are rationally formal.


References [Enhancements On Off] (What's this?)

  • 1. Anders Björner, Subspace arrangements, First European Congress of Mathematics, Vol. I (Paris, 1992), Progr. Math., vol. 119, Birkhäuser, Basel, 1994, pp. 321-370. MR 1341828 (96h:52012)
  • 2. Anders Björner and Volkmar Welker, The homology of ``$ k$-equal'' manifolds and related partition lattices, Adv. Math. 110 (1995), no. 2, 277-313. MR 1317619 (95m:52029)
  • 3. William Brockman and Bruce E. Sagan, The $ k$-consecutive arrangements, lecture slides, http://www.mth.msu.edu/$ \tilde{ }$sagan/Slides/list.html.
  • 4. C. De Concini and C. Procesi, Wonderful models of subspace arrangements, Selecta Math. (N.S.) 1 (1995), no. 3, 459-494. MR 1366622 (97k:14013)
  • 5. Graham Denham and Alexander I. Suciu, Moment-angle complexes, monomial ideals and Massey products, Pure Appl. Math. Q. 3 (2007), no. 1, 25-60. MR 2330154
  • 6. E. M. Feichtner and S. Yuzvinsky, Formality of the complements of subspace arrangements with geometric lattices, Zap. Nauchn. Sem. S.-Peterburg. Otdel. Mat. Inst. Steklov. (POMI) 326 (2005), Teor. Predst. Din. Sist. Komb. i Algoritm. Metody. 13, 235-247, 284. MR 2183223 (2007a:55021)
  • 7. Jelena Grbić and Stephen Theriault, The homotopy type of the complement of a coordinate subspace arrangement, Topology 46 (2007), no. 4, 357-396. MR 2321037
  • 8. Dmitry N. Kozlov, A class of hypergraph arrangements with shellable intersection lattice, J. Combin. Theory Ser. A 86 (1999), no. 1, 169-176. MR 1682970 (2000e:52023)
  • 9. Matthew S. Miller and Max Wakefield, Edge colored hypergraphic arrangements, Pure Appl. Math. Q. 8 (2012), no. 3, 761-783, to appear.
  • 10. Irena Peeva, Vic Reiner, and Volkmar Welker, Cohomology of real diagonal subspace arrangements via resolutions, Compositio Math. 117 (1999), no. 1, 99-115. MR 1693007 (2001c:13021)
  • 11. Sergey Yuzvinsky, Rational model of subspace complement on atomic complex, Publ. Inst. Math. (Beograd) (N.S.) 66(80) (1999), 157-164, Geometric combinatorics (Kotor, 1998). MR 1765044 (2002b:52026)
  • 12. -, Small rational model of subspace complement, Trans. Amer. Math. Soc. 354 (2002), no. 5, 1921-1945 (electronic). MR 1881024 (2003a:52030)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2010): 52C35, 55R80

Retrieve articles in all journals with MSC (2010): 52C35, 55R80


Additional Information

Matthew Miller
Affiliation: Department of Mathematics, Vassar College, Poughkeepsie, New York 12604
Email: mamiller@vassar.edu

Max Wakefield
Affiliation: Department of Mathematics, United States Naval Academy, Annapolis, Maryland 21402
Email: wakefiel@usna.edu

DOI: https://doi.org/10.1090/S0002-9939-2011-11009-8
Received by editor(s): October 15, 2009
Published electronically: April 5, 2011
Additional Notes: The second author has been supported by NSF grant No. 0600893, the NSF Japan program, and the Office of Naval Research.
Communicated by: Jim Haglund
Article copyright: © Copyright 2011 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

American Mathematical Society