Stiefel-Whitney classes and immersions of orientable and Spin manifolds
Algebraic Topology
2021-03-23 v3
Abstract
We determine a nice simple formula for the largest Euclidean space for which there is an orientable n-manifold with a nonimmersion detected by Stiefel-Whitney classes. For Spin manifolds, we prove the analogue of the upper bound and establish the complete answer for n<24 and n=33,34. Results similar to many of these were obtained some 50 years ago, but in a much less tractable form. The sharp results for Spin manifolds require detailed calculations of ko-homology groups of mod-2 Eilenberg-MacLane spaces.
Keywords
Cite
@article{arxiv.2011.00974,
title = {Stiefel-Whitney classes and immersions of orientable and Spin manifolds},
author = {Donald M. Davis and W. Stephen Wilson},
journal= {arXiv preprint arXiv:2011.00974},
year = {2021}
}
Comments
Some new results. Some minor corrections. Addition of coauthor