Comparing cohomology obstructions
Algebraic Topology
2010-08-11 v1
Abstract
We show that three different kinds of cohomology - Baues-Wirsching cohomology, the (S,O)-cohomology of Dwyer-Kan, and the Andre-Quillen cohomology of a Pi-algebra - are isomorphic, under certain assumptions. This is then used to identify the cohomological obstructions in three general approaches to realizability problems: the track category version of Baues-Wirsching, the diagram rectifications of Dwyer-Kan-Smith, and the Pi-Algebra realization of Dwyer-Kan-Stover. Our main tool in this identification is the notion of a mapping algebra: a simplicially enriched version of an algebra over a theory.
Cite
@article{arxiv.1008.1712,
title = {Comparing cohomology obstructions},
author = {Hans-Joachim Baues and David Blanc},
journal= {arXiv preprint arXiv:1008.1712},
year = {2010}
}