A new equivariant cohomology ring (Q2193039)

Algebraic invariants of orbifolds constructed by push-pullback methods are numerous, as Chen-Ruang cohomology, virtual cohomology, stringy and twisted K-theory, among others. In this work motivated by the equivariant Gromov-Witten invariants, the authors produce a new cohomology theory associated to a global quotient \((X,G)\) given by the action of a connected compact Lie group \(G\) over a compact almost complex manifold \(X\). This construction is achieved considering \(m\)-sectors of \((X,G)\) which conform the \(m\)-inertia orbifolds for \(m\geq 2\). They produce \(m\)-products identifying the \(m\)-sectors with some moduli spaces given by orbifold coverings mapped to \((X,G)\) which preserve the holomorphic and equivariant structure in a certain sense. An obstruction bundle is produced over the moduli spaces giving the associative properties for the \(m\)-products and some Frobenius property.