A successful generalization of phantom map theory to the equivariant case for all compact Lie groups is obtained in this paper. One of the key observations is the discovery of the fact that homotopy fiber of equivariant completion splits as product of equivariant Eilenberg-Maclane spaces which seems impossible at first sight by the example of Triantafillou[19].

We find presentations by generators and relations for the equivariant quantum cohomology of the Grassmannian. For these presentations, we also find determinantal formulae for the equivariant quantum Schubert classes. To prove this, we use the theory of factorial Schur functions and a characterization of the equivariant quantum cohomology ring.

Consider independent fair coin-flips at each site of the lattice Z d. A translation-equivariant matching rule is a perfect matching of heads to tails that commutes with translations of Z d and is given by a deterministic function of the coin-flips. Let Z Φ be the distance from the origin to its partner, under the translation-equivariant matching rule Φ. Holroyd and Peres [9] asked what is the o...

The results of a previous paper on the equivariant homotopy theory of crossed complexes are generalised from the case of a discrete group to general topological groups. The principal new ingredient necessary for this is an analysis of homotopy coherence theory for crossed complexes, using detailed results on the appropriate Eilenberg–Zilber theory, and of its relation to simplicial homotopy coh...

The simultaneous partition problems are classical problems of the combinatorial geometry which have the natural flavor of the equivariant topology. The k-fan partition problems have attracted a lot of attention [1], [2], [17], [11] and forced some hard concrete combinatorial calculations in the equivariant cohomology [3]. These problems can be reduced, by a beautiful scheme of [1], to a ”typica...

Introduced by Borel in the late 1950’s, equivariant cohomology encodes information about how the topology of a space interacts with a group action. Quite some time passed before algebraic geometers picked up on these ideas, but in the last twenty years, equivariant techniques have found many applications in enumerative geometry, Gromov-Witten theory, and the study of toric varieties and homogen...

We study D-branes and Ramond-Ramond fields on global orbifolds of Type II string theory with vanishing H-flux using methods of equivariant K-theory and K-homology. We illustrate how Bredon equivariant cohomology naturally realizes stringy orbifold cohomology. We emphasize its role as the correct cohomological tool which captures known features of the low-energy effective field theory, and which...

For a smooth manifold equipped with a compact Lie group action, we construct an equivariant cohomology theory which takes values in a vertex algebra, and contains the classical equivariant cohomology as a subalgebra. The main idea is to synthesize the algebraic approach to the classical equivariant cohomology theory due to H. Cartan and Guillemin-Sternberg, with the chiral de Rham algebra of Ma...

We identify and examine a generalization of topological sigma models suitable for coupling to topological open strings. The targets are Kähler manifolds with a real structure, i.e. with an involution acting as a complex conjugation, compatible with the Kähler metric. These models satisfy axioms of what might be called “equivariant topological quantum field theory,” generalizing the axioms of to...