In knot theory, it is well-known that two links in the Euclidean 3-space are ambient isotopic if and only if they are related by a finite number of combinatorial moves along 2-simplices. This fact is generalized for submanifolds in a manifold whose codimensions are positive.
Seiichi KAMADA. Akio KAWAUCHI. Takao MATUMOTO. "Combinatorial moves on ambient isotopic submanifolds in a manifold." J. Math. Soc. Japan 53 (2) 321 - 331, April, 2001. https://doi.org/10.2969/jmsj/05320321