English

On the zero-divisor-cup-length of spaces of oriented isometry classes of planar polygons

Algebraic Topology 2016-03-18 v3

Abstract

Using information about the rational cohomology ring of the space of oriented isometry classes of planar n-gons with specified side lengths, we obtain bounds for the zero-divisor-cup-length (zcl) of these spaces, which provide lower bounds for their topological complexity (TC). In many cases our result about the cohomology ring is complete and we determine the precise zcl. We find that there will usually be a significant gap between the bounds for TC implied by zcl and dimensional considerations.

Keywords

Cite

@article{arxiv.1511.05783,
  title  = {On the zero-divisor-cup-length of spaces of oriented isometry classes of planar polygons},
  author = {Donald M. Davis},
  journal= {arXiv preprint arXiv:1511.05783},
  year   = {2016}
}

Comments

Replaces a paper entitled "On the cohomology ring of oriented isometry classes of planar polygons." Change of emphasis, significant corrections. Uses rational cohomology rather than mod 2. This version resubmitted for publication, following a very perceptive referee's report