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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