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An action of a finite group on an $n$-cell without stationary points

1959
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Bulletin of the American Mathematical Society
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If G is a transformation group on a space X, then x(~X is a stationary point if gx = x for every g£G. It has been an open problem, proposed by Smith [5] and by Montgomery [l, Problem 39], to determine whether every compact Lie group acting on a cell or on Euclidean space has a stationary point. Smith [4; 5] has shown the answer to be in the affirmative in case G is a toral group or a finite group of prime power order. In this note we give a simplicial action of A^ the group of even permutations

doi:10.1090/s0002-9904-1959-10282-2
fatcat:r3wf6y7rw5borlqya2tjqzrheq