Subdivisions and transgressive chains
Abstract
Combinatorial transgressions are secondary invariants of a space admitting triangulations. They arise from subdivisions and are analogous to transgressive forms such as those arising in Chern-Weil theory. Unlike combinatorial characteristic classes, combinatorial transgressions have not been previously studied. First, this article characterizes transgressions that are path-independent of subdivision sequence. The result is obtained by using a cohomology on posets that is shown to be equivalent to higher derived functors of the inverse (or projective) limit over the opposite poset. Second, a canonical local formula is demonstrated for a particular combinatorial transgression: namely, that relative the difference of Poincar\'{e} duals to the Euler class.
Cite
@article{arxiv.0806.0390,
title = {Subdivisions and transgressive chains},
author = {Jer-Chin Chuang},
journal= {arXiv preprint arXiv:0806.0390},
year = {2008}
}