Manifolds admitting a continuous cancellative binary operation are orientable
classification
🧮 math.GT
math.GR
keywords
binarycancellativecontinuousoperationadmittingorientableadmitsanswers
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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.
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