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)
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