Rational homotopy type of subspace arrangements with a geometric lattice

Debongnie, Gery
(2008) Proceedings of the American Mathematical Society — Vol. 136, n° 6, p. 2245-2252 (2008)

Files

S0002-9939-08-09312-X.pdf
  • Open Access
  • Adobe PDF
  • 165.21 KB
Download

Details

Authors
  • Debongnie, GeryUCLouvain
    Author
Abstract
Let A = {x(1),..., x(n)} be a subspace arrangement with a geometric lattice such that codim(x) = 2 for every x. A. Using rational homotopy theory, we prove that the complement M(A) is rationally elliptic if and only if the sum x1/1 +... + x1/n is a direct sum. The homotopy type of M(A) is also given: it is a product of odd-dimensional spheres. Finally, some other equivalent conditions are given, such as Poincare duality. Those results give a complete description of arrangements (with a geometric lattice and with the codimension condition on the subspaces) such that M(A) is rationally elliptic, and show that most arrangements have a hyperbolic complement.
Affiliations

Citations

  • APA
  • Chicago
  • FWB

Debongnie, G. (2008). Rational homotopy type of subspace arrangements with a geometric lattice. Proceedings of the American Mathematical Society, 136(6), 2245-2252. https://doi.org/10.1090/S0002-9939-08-09312-X (Original work published 2008)