Manifolds admitting a continuous cancellative binary operation are orientable
Geometric Topology
2016-06-23 v1 Group Theory
Abstract
We prove that a topological manifold (possibly with boundary) admitting a continuous cancellative binary operation is orientable. This implies that the M\"obius band admits no cancellative continuous binary operation. This answers a question posed by the second author in 2010.
Cite
@article{arxiv.1503.08993,
title = {Manifolds admitting a continuous cancellative binary operation are orientable},
author = {Taras Banakh and Igor Guran and Alex Ravsky},
journal= {arXiv preprint arXiv:1503.08993},
year = {2016}
}
Comments
5 pages