I have a feeling that I have seen some kind of theory of linking and intersection that applies in spaces that are not manifolds. I've found two kinds of theories in the books I've checked:
1) intersection product of homology classes, defined in terms of Poincare duality,
2) linking numbers defined for disjoint subsets of $\mathbb{R}^n$ using the vector space structure of $\mathbb{R}^n$.
What I really want to do is to talk about intersection/linking of subcomplexes of a finite simplicial complex. Can anyone point me to a reference?
Best Answer
I'm not quite sure if this is what you're thinking of, but intersection homology has a good theory of intersection products for simplicial pseudomanifolds. See Goresky-MacPherson, "Intersection Homology Theory"