Almost Global Homotopy Theory
Abstract
In this paper we develop the definition of a global orthogonal spectrum and its unitary version. It relates equivariant spectra by equivariant weak equivalence in a coherent way. This category of global spectra has a model structure Quillen equivalent to the global model structure on orthogonal spectra. We also show that there is a large family of equivariant cohomology theories, including quasi-elliptic cohomology, that can be globalized in the new context. Starting from one global ring spectrum, we can construct infinitely many distinct global ring spectra. Moreover, in light of the results in this paper, we ask whether we have the conjecture that the globalness of a cohomology theory is completely determined by the formal component of its divisible group and when the tale component of it varies the globalness does not change.
Cite
@article{arxiv.1809.08921,
title = {Almost Global Homotopy Theory},
author = {Zhen Huan},
journal= {arXiv preprint arXiv:1809.08921},
year = {2018}
}
Comments
22 pages. We proved that there is a global model structure on the new theory, not only $Fin-$global model structure