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A fixed-point theorem is a result saying that a function $F$ will have at least one fixed point (a point $x$ for which $F(x) = x$), under some conditions on $F$ that can be stated in general terms.

20 votes

Do finite groups acting on a ball have a fixed point?

Bob Oliver classified the finite groups that act without a global fixed point on some sufficiently high-dimensional disk. The conditions are somewhat complicated to state. But for finite abelian group …
Allan Edmonds's user avatar