Some new homology and cohomology theories of manifolds and orbifolds

Dominic Joyce

For each manifold or effective orbifold $Y$ and commutative ring $R$, we define a new homology theory $M{H}_{\ast }(Y;R)$, $M$-$homology$, and a new cohomology theory $M{H}^{\ast }(Y;R)$, $M$-$coh…