Ambient Isotopy

An ambient isotopy from an embedding of a Manifold in to another is a Homotopy of selfDiffeomorphisms (or Isomorphisms, or piecewise-linear transformations,etc.) of , starting at the Identity Map, such that the ``last'' Diffeomorphism compounded with the firstembedding of is the second embedding of . In other words, an ambient isotopy is like an Isotopy except thatinstead of distorting the embedding, the whole ambient Space is being stretched and distorted and the embedding isjust ``coming along for the ride.'' For Smooth Manifolds, a Map isIsotopic Iff it is ambiently isotopic.

For Knots, the equivalence of Manifolds under continuous deformation is independent ofthe embedding Space. Knots of opposite Chirality have ambient isotopy, but notRegular Isotopy.

References

Hirsch, M. W. Differential Topology. New York: Springer-Verlag, 1988.

• Monica Set
• Monic Polynomial
• Monkey and Coconut Problem
• Monkey Saddle
• Monochromatic Forced Triangle
• Monodromy
• Monodromy Group
• Monodromy Theorem
• Monogenic Function
• Monohedral Tiling
• Monoid
• Monomial
• Monomino
• Monomorph
• Monomorphism
• Monotone
• Monotone Decreasing
• Monotone Increasing
• Monotonic Function
• Monotonic Sequence
• Monotonic Voting
• Monster Group
• Monte Carlo Integration
• Monte Carlo Method
• Montel's Theorem