English

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

R2 v1 2026-06-22T09:06:43.851Z