Journal of Lie Theory

no. 4
Manifolds Admitting a Continuous Cancellative Binary Operation are Orientable
Journal of Lie Theory, Volume 26 (2016) no. 4, pp. 1177-1185
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.
DOI: 10.5802/jolt.928
Classification: 22A15, 57N37
Keywords: Cancellative binary operation, orientable manifold 
@article{JOLT_2016_26_4_a10,
     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},
     year = {2016},
     volume = {26},
     number = {4},
     doi = {10.5802/jolt.928},
     zbl = {1354.22003},
     url = {https://jolt.centre-mersenne.org/articles/10.5802/jolt.928/}
}
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T. Banakh; I. Guran; A. Ravsky. Manifolds Admitting a Continuous Cancellative Binary Operation are Orientable. Journal of Lie Theory, Volume 26 (2016) no. 4, pp. 1177-1185. doi: 10.5802/jolt.928

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