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Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In mathematics, the Kervaire invariant, named for Michel Kervaire, is defined in geometric topology. It is an invariant of an (4k+2)-dimensional (singly even-dimensional) framed differentiable manifold M, taking values in the 2-element group Z/2Z = {0,1}. The Kervaire invariant is defined as the Arf invariant of the skew-quadratic form on the middle dimensional homology group.