On a new geometric homology theory
Abstract
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 chainlevel theories. We will develop further of this theory in our sequel paper.
 Publication:

arXiv eprints
 Pub Date:
 April 2020
 arXiv:
 arXiv:2004.07698
 Bibcode:
 2020arXiv200407698Y
 Keywords:

 Mathematics  Algebraic Topology;
 Mathematics  Geometric Topology
 EPrint:
 Comments are appreciated !. arXiv admin note: text overlap with arXiv:0709.3874 by other authors