For the standard embedded torus, the skew-symmetric form is given by (with respect to the standard symplectic basis), and the skew-quadratic refinement is given by with respect to this basis: : the basis curves don't self-link; and : a (1,1) self-links, as in the Hopf fibration. This form thus has Arf invariant 0 (most of its elements have norm 0; it has isotropy index 1), and thus the standard embedded torus has Kervaire invariant 0.
Read more about this topic: Kervaire Invariant
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Famous quotes containing the word examples:
“No rules exist, and examples are simply life-savers answering the appeals of rules making vain attempts to exist.”
—André Breton (18961966)
“In the examples that I here bring in of what I have [read], heard, done or said, I have refrained from daring to alter even the smallest and most indifferent circumstances. My conscience falsifies not an iota; for my knowledge I cannot answer.”
—Michel de Montaigne (15331592)
“It is hardly to be believed how spiritual reflections when mixed with a little physics can hold peoples attention and give them a livelier idea of God than do the often ill-applied examples of his wrath.”
—G.C. (Georg Christoph)