Lesson plan
2-sided
In mathematics, specifically in topology of manifolds, a compact codimension-one submanifold F of a manifold M is said to be 2-sided in M when there is an embedding :: h\colon F\times [-1,1]\to M with h(x,0)=x for each x\in F and :: h(F\times [-1,1])\cap \partial M=h(\partial F\times [-1,1]) . In other words, if its normal bundle is trivial. 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.
Article summary
In mathematics, specifically in topology of manifolds, a compact codimension-one submanifold F of a manifold M is said to be 2-sided in M when there is an embedding :: h\colon F\times [-1,1]\to M with h(x,0)=x for each x\in F and :: h(F\times [-1,1])\cap \partial M=h(\partial F\times [-1,1]) . In other words, if its normal bundle is trivial. 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.
Key claims
No claims recorded.
Discussion questions
- Summarise the article in your own words. Which single claim would you verify first, and why?
- Which claim in this article is most likely to be revised as the sources update? How would you check its current status?
- If two sources disagreed about one of these facts, what would you need in order to trust one over the other?
Bibliography
No sources recorded.
Key claims and bibliography are generated from the same tracked claims and sources as the article page.