On Colimits and Model Structures in Various Categories of Manifolds
Algebraic Topology
2024-08-27 v1
Abstract
After explaining the importance of model categories in abstract homotopy theory, we provide concrete examples demonstrating that various categories of manifolds do not have all finite colimits, and hence cannot be model categories. We then consider various enlargements of our categories of manifolds, culminating in categories of presheaves. We explain how to produce model structures on these enlarged categories, culminating with answering an open problem involving Poincar\'{e} spaces.
Cite
@article{arxiv.2405.15511,
title = {On Colimits and Model Structures in Various Categories of Manifolds},
author = {David White},
journal= {arXiv preprint arXiv:2405.15511},
year = {2024}
}
Comments
This paper is mostly expository but has recently generated some interest, so I am putting it on arXiv. I greatly expanded it from the version that has been on my webpage for several years, and have added the discussion of Poincare spaces