A bstract In this note we review a construction of BPS Hilbert space in an effective supersymmetric quiver theory with 4 supercharges. We argue abstractly that contains elements equivariant generalized cohomology $$ {E}_G^{\ast}\left(-\right) E G ∗ <mml:mfenc...

Let (R,m) be a local ring, I a proper ideal of R and M a finitely generated R-module of dimension d. We discuss the local homology modules of H I (M). When M is Cohen-Macaulay, it is proved that H d m(M) is co-CohenMacaulay of N.dimension d and H x d (H m(M)) = M̂ where x = (x1, . . . , xd) is a system of parameters for M . 2000 Mathematics Subject Classification: 13C14, 13D45

Let ( X , J ) be an almost complex manifold with a (smooth) involution σ : → such that Fix ≠ ∅ . Assume is conjugation, i.e., the differential of anti-commutes The space P m = S × / ∼ where v x − was referred to as generalized Dold manifold. above definition admits obvious generalization much wider class spaces are arbitrary topological spaces. resulting will called space. When and CW complexes...

We explain how the approach of André and Quillen to defining cohomology and homology as suitable derived functors extends to generalized (co)homology theories, and how this identification may be used to study the relationship between them.

We construct a ring structure on complex cobordism tensored with Q, which is related to the usual ring structure as quantum cohomology is related to ordinary cohomology. The resulting object defines a generalized two-dimensional topological field theory taking values in a category of spectra.