Effective topological complexity of orientable-surface groups
Algebraic Topology
2020-03-04 v2
Abstract
We use rewriting systems to spell out cup-products in the (twisted) cohomology groups of a product of surface groups. This allows us to detect a non-trivial obstruction bounding from below the effective topological complexity of an orientable surface with respect to its antipodal involution. Our estimates are at most one unit from being optimal, and are closely related to the (regular) topological complexity of non-orientable surfaces.
Cite
@article{arxiv.1907.10212,
title = {Effective topological complexity of orientable-surface groups},
author = {Natalia Cadavid-Aguilar and Jesús González},
journal= {arXiv preprint arXiv:1907.10212},
year = {2020}
}
Comments
27 pages. This new version of the paper includes a detailed application of the cohomology calculations to the effective topological complexity of oriented surfaces