A regular homotopy between two immersions f and g from a manifold M to a manifold N is defined to be a differentiable function H : M × → N such for all t in the function Ht : M → N defined by Ht(x) = H(x, t) for all x ∈ M is an immersion, with H0 = f, H1 = g. A regular homotopy is thus a homotopy through immersions.
Read more about this topic: Immersion (mathematics)
Famous quotes containing the word regular:
““I couldn’t afford to learn it,” said the Mock Turtle with a sigh. “I only took the regular course.”
“What was that?” inquired Alice.
“Reeling and Writhing, of course, to begin with,” the Mock Turtle replied; “and then the different branches of Arithmetic—Ambition, Distraction, Uglification, and Derision.”
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—Lewis Carroll [Charles Lutwidge Dodgson] (1832–1898)