Suppose I have a cartwheel-like structure minus the rim where all the spokes are made up of infinite chains of tori, say my structure has n such spokes, how many "ends" (in the topological sense) does this 3D surface have?
Is such a surface homeomorphic to all surfaces made up of infinitely many tori with that number of ends? If not, how might I count the number of 3D surfaces up to homeomorphism that are made up of gluing together infinitely many tori?
Thank you.