Geodesic
Manifolds Admitting a Continuous Cancellative Binary Operation are Orientable
Journal of Lie theory, Tome 26 (2016) no. 4, pp. 1177-1185
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Generalizing the well-known result on the orientability of Lie groups, we prove that a topological manifold (possibly with boundary) admitting a continuous cancellative binary operation is orientable. This implies that the Möbius band admits no cancellative continuous binary operation and answers a question posed by the second author in 2010.
Classification : 22A15, 57N37
Mots-clés : Cancellative binary operation, orientable manifold 
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     author = {T. Banakh and I. Guran and A. Ravsky},
     title = {Manifolds {Admitting} a {Continuous} {Cancellative} {Binary} {Operation} are {Orientable}},
     journal = {Journal of Lie theory},
     pages = {1177--1185},
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     volume = {26},
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T. Banakh; I. Guran; A. Ravsky. Manifolds Admitting a Continuous Cancellative Binary Operation are Orientable. Journal of Lie theory, Tome 26 (2016) no. 4, pp. 1177-1185. http://geodesic.mathdoc.fr/item/JLT_2016_26_4_JLT_2016_26_4_a10/