Rational homotopy type of subspace arrangements with a geometric lattice

Author:
Gery Debongnie

Journal:
Proc. Amer. Math. Soc. **136** (2008), 2245-2252

MSC (2000):
Primary 55P62

Published electronically:
February 14, 2008

MathSciNet review:
2383531

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Abstract: Let be a subspace arrangement with a geometric lattice such that for every . Using rational homotopy theory, we prove that the complement is rationally elliptic if and only if the sum is a direct sum. The homotopy type of is also given: it is a product of odd-dimensional spheres. Finally, some other equivalent conditions are given, such as Poincaré duality. Those results give a complete description of arrangements (with a geometric lattice and with the codimension condition on the subspaces) such that is rationally elliptic, and show that most arrangements have a hyperbolic complement.

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Additional Information

**Gery Debongnie**

Affiliation:
Université Catholique de Louvain, Departement de Mathematique, Chemin du Cyclotron, 2, B-1348 Louvain-la-Neuve, Belgium

Email:
debongnie@math.ucl.ac.be

DOI:
https://doi.org/10.1090/S0002-9939-08-09312-X

Received by editor(s):
January 31, 2007

Published electronically:
February 14, 2008

Additional Notes:
The author is an “Aspirant” of the “Fonds National pour la Recherche Scientifique” (FNRS), Belgium.

Communicated by:
Paul Goerss

Article copyright:
© Copyright 2008
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication.