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Journal of Lie Theory 26 (2016), No. 4, 1177--1185
Copyright Heldermann Verlag 2016



Manifolds Admitting a Continuous Cancellative Binary Operation are Orientable

Taras Banakh
Faculty of Mechanics and Mathematics, Ivan Franko National University, Lviv 79000, Ukraine
t.o.banakh@gmail.com

Ivan Guran
Faculty of Mechanics and Mathematics, Ivan Franko National University, Lviv 79000, Ukraine
igor_guran@yahoo.com

Alex Ravsky
Pidstryhach Institute, National Academy of Sciences, 3-b Naukova Street, Lviv 79060, Ukraine
oravsky@mail.ru



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.

Keywords: Cancellative binary operation, orientable manifold.

MSC: 22A15, 57N37

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