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John Francis
Q: What are (co)homology theories, geometrically? Vector bundles represent
K-theory classes; manifolds represent bordism classes. The seasoned
topology grad student can construct a menagerie of other (co)homology
theories by homotopy methods, but much of the significance of these three
original theories is they conjoin homotopy and geometry. This prompts us to
ask: what is the answer to Q? A: (Co)bordism with singularities.
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