The realization space of an unstable coalgebra
Abstract
Unstable coalgebras over the Steenrod algebra form a natural target category for singular homology with prime field coefficients. The realization problem asks whether an unstable coalgebra is isomorphic to the homology of a topological space. We study the moduli space of such realizations and give a description of this in terms of cohomological invariants of the unstable coalgebra. This is accomplished by a thorough comparative study of the homotopy theories of cosimplicial unstable coalgebras and of cosimplicial spaces.
Cite
@article{arxiv.1409.0410,
title = {The realization space of an unstable coalgebra},
author = {Georg Biedermann and Georgios Raptis and Manfred Stelzer},
journal= {arXiv preprint arXiv:1409.0410},
year = {2017}
}
Comments
118 pages. Final version ; accepted for publication in Ast\'erisque. The presentation of the material is reorganized and generally improved. More details are added in some proofs and some corrections are made, especially in Section 7 and Appendix A. Some issues concerning basepoints are resolved and the module actions in the spiral exact sequence are explained in detail