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.Comment: Comments are appreciated !. arXiv admin note: text overlap with
arXiv:0709.3874 by other author