We prove that the Brin-Thompson groups sV, also called higher dimensional
Thompson's groups, are of type F_\infty for all natural numbers s. This result
was previously shown for s up to 3, by considering the action of sV on a
naturally associated space. Our key step is to retract this space to a subspace
sX which is easier to analyze.Comment: Final version, in Pacific J. Math., 10 pages, 4 figure