Higher Dimensions
One can analogously define concordance for any two submanifolds . In this case one considers two submanifolds concordant if there is a cobordism between them in i.e., if there is a manifold with boundary whose boundary consists of and
This higher dimensional concordance is a relative form of cobordism – it requires two submanifolds to be not just abstractly cobordant, but "cobordant in N".
Read more about this topic: Link Concordance
Famous quotes containing the words higher and/or dimensions:
“Every man wants a woman to appeal to his better side, his nobler instincts and his higher nature—and another woman to help him forget them.”
—Helen Rowland (1875–1950)
“Words are finite organs of the infinite mind. They cannot cover the dimensions of what is in truth. They break, chop, and impoverish it.”
—Ralph Waldo Emerson (1803–1882)