Rational Homotopy Type of Subspace Arrangements with a Geometric Lattice
نویسنده
چکیده
Let A = {x1, . . . , xn} 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 x 1 + . . . + x 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 Poincaré duality. Those results give a complete description of arrangements (with geometric lattice and with the codimension condition on the subspaces) such that M(A) is rationally elliptic, and show that most arrangements have an hyperbolic complement.
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