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cianfa72
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No more time...I'm definitly wrong.
I Smooth coordinate chart on spacetime manifold
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- Thread starter cianfa72
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- Coordinate Smooth
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The discussion centers on the definition of a smooth coordinate chart for a manifold, particularly in the context of spacetime. Participants express confusion over the lack of an invariant definition, arguing that a coordinate system's smoothness depends on existing structures. It is clarified that a smooth chart is defined in relation to a smooth manifold structure, which includes a maximal atlas where transformations between charts are smooth. The conversation also touches on the challenges of defining smooth structures on specific surfaces, like a cube, emphasizing that while a smooth structure can be defined, compatibility with certain embeddings may not be possible. Ultimately, the dialogue highlights the complexities of differentiable structures and their dependence on the underlying topology of the manifold.