In tomorrow’s lecture we will catch a first glimpse of the idea of *manifolds*, which are pretty central to differential geometry. Rather than giving a formal definition in the smooth case, we’ll introduce a notion of *discrete manifolds* that capture the most important ideas. These discrete manifolds build on the idea of a *simplicial complex*, introduced in the previous lecture.

## 1 thought on “Lecture 2B: Introduction to Manifolds”

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If two bodies are interacting with a common face, as it happens in many surface tension related phenomena, then in that condition 3 facets meet at a single edge. There exist many such edges and make something called three-phase-contact line. Can we call this complex as manifold? Can we apply all the tools that you are discussing in currently uploaded lectures?

I have used Ken Brakke’s Surface Evolver so my question is based on that experience.