The Cohomology Rings of Complements of Subspace Arrangements

On Cohomology Algebras of Complex Subspace Arrangements

The integer cohomology algebra of the complement of a complex subspace arrangement with geometric intersection lattice is completely determined by the combinatorial data of the arrangement. We give a combinatorial presentation of the cohomology algebra in the spirit of the Orlik-Solomon result on the cohomology algebras of complex hyperplane arrangements. Our methods are elementary: we work wit...

Ring structures of mod p equivariant cohomology rings and ring homomorphisms between them

In this paper, we consider a class of connected oriented (with respect to Z/p) closed G-manifolds with a non-empty finite fixed point set, each of which is G-equivariantly formal, where G = Z/p and p is an odd prime. Using localization theorem and equivariant index, we give an explicit description of the mod p equivariant cohomology ring of such a G-manifold in terms of algebra. This makes ...

Cohomology Algebras of Complex Subspace Arrangements 3

The Ring Structure on the Cohomology of Coordinate Subspace Arrangements

Homotopy Types of Complements of 2-arrangements in R

We study the homotopy types of complements of arrangements of n transverse planes in R4, obtaining a complete classification for n ≤ 6, and lower bounds for the number of homotopy types in general. Furthermore, we show that the homotopy type of a 2-arrangement in R4 is not determined by the cohomology ring, thereby answering a question of Ziegler. The invariants that we use are derived from the...