Local: turn left, then turn right Global: turn North, then turn East Connection: Pointing North on Long Island is not the same as pointing North in Seattle.
Manifolds: Zoom in close enough and it looks Euclidian. What's an intuition/heuristic you all use for concepts whose formal definitions are rather complicated?
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oh wow I like that one a lot
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Simply connected domain: the one without holes
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I like that one!
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Fiber bundles: Stick a copy of a shape (the fiber) onto every point of another shape (the base) such that it varies continuously (no sudden or big changes).
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nice one!
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Modules over commutative rings: something like a vector space, aka free module (viewed geometrically as an N-space), but modded out by a submodule ("wrapped", much like Z/nZ resembles a circle but with only n equally spaced points).
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I've always kind of thought of them as vector spaces too!
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deRham cohomology: vector field with curl=0 pointing round a linelike hole, vector field with div=0 pointing away from a pointlike hole.
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yes I know it's really forms, who cares
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