Restricting cohomology classes to disk and segment configuration spaces
Metric Geometry
2016-08-24 v1 Algebraic Topology
Combinatorics
Abstract
The configuration space of n labeled disks of radius r inside the unit disk is denoted Conf_{n, r}(D^2). We study how the cohomology of this space depends on r. In particular, given a cohomology class of Conf_{n, 0}(D^2), for which r does its restriction to Conf_{n, r}(D^2) vanish? A related question: given the configuration space Seg_{n, r}(D^2) of n labeled, oriented segments of length r, it has a map to (S^1)^n that records the direction of each segment. For which r does this angle map have a continuous section? The paper consists of a collection of partial results, and it contains many questions and conjectures.
Cite
@article{arxiv.1608.06612,
title = {Restricting cohomology classes to disk and segment configuration spaces},
author = {Hannah Alpert},
journal= {arXiv preprint arXiv:1608.06612},
year = {2016}
}