2-sided

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In mathematics, specifically in topology of manifolds, a compact codimension-one submanifold ${\displaystyle F}$ of a manifold ${\displaystyle M}$ is said to be 2-sided in ${\displaystyle M}$ when there is an embedding

${\displaystyle h\colon F\times [-1,1]\to M}$

with ${\displaystyle h(x,0)=x}$ for each ${\displaystyle x\in F}$ and

${\displaystyle h(F\times [-1,1])\cap \partial M=h(\partial F\times [-1,1])}$.

In other words, if its normal bundle is trivial.^[1]

This means, for example that a curve in a surface is 2-sided if it has a tubular neighborhood which is a cartesian product of the curve times an interval.

A submanifold which is not 2-sided is called 1-sided.