Morse Functions
Suppose that is a Morse function on an -dimensional manifold, and suppose that is a critical value with exactly one critical point in its preimage. If the index of this critical point is, then the level-set is obtained from by a -surgery. The inverse image defines a cobordism that can be identified with the trace of this surgery.
Read more about this topic: Cobordism
Famous quotes containing the word functions:
“When Western people train the mind, the focus is generally on the left hemisphere of the cortex, which is the portion of the brain that is concerned with words and numbers. We enhance the logical, bounded, linear functions of the mind. In the East, exercises of this sort are for the purpose of getting in tune with the unconscious—to get rid of boundaries, not to create them.”
—Edward T. Hall (b. 1914)