On the unordered configuration space C(RP^n,2)
Algebraic Topology
2019-05-27 v1
Abstract
We prove that, if n is a 2-power, the unordered configuration space C(RP^n,2) cannot be immersed in R^{4n-2} nor embedded as a closed subspace of R^{4n-1}, optimal results, while if n is not a 2-power, C(RP^n,2) can be immersed in R^{4n-3}. We also obtain cohomological lower bounds for the topological complexity of C(RP^n,2), which are nearly optimal when n is a 2-power. We also give a new description of the mod-2 cohomology algebra of the Grassmann manifold G_{n+1,2}.
Cite
@article{arxiv.1905.10339,
title = {On the unordered configuration space C(RP^n,2)},
author = {Donald M. Davis},
journal= {arXiv preprint arXiv:1905.10339},
year = {2019}
}