On a new geometric homology theory

In this note we present a new homology theory, we call it geometric homology theory (or GHT for brevity). We prove that the homology groups of GHT are isomorphic to the singular homology groups, which solves a Conjecture of Voronov. GHT has several nice properties compared with singular homology, which makes itself more suitable than singular homology in some situations, especially in chain-level theories. We will develop further of this theory in our sequel paper.