Yes, a lot of "applied topology" nowadays is of this sort: start with something, draw a simplicial complex, compute homology. Big whoop. Note that all this goes way back before Eilenberg (and even Poincaré). Betti knew how to do it.
His name was Betty? No wonder it's called Homology. I guess the question, to make meaningful the "applied" part, is if once you've computed the homology you've gained some new and improved understanding of whatever it is being studied. Can either of you, JJ and AI, think of some examples of such?
2 comments:
Yes, a lot of "applied topology" nowadays is of this sort: start with something, draw a simplicial complex, compute homology. Big whoop. Note that all this goes way back before Eilenberg (and even Poincaré). Betti knew how to do it.
His name was Betty? No wonder it's called Homology.
I guess the question, to make meaningful the "applied" part, is if once you've computed the homology you've gained some new and improved understanding of whatever it is being studied. Can either of you, JJ and AI, think of some examples of such?
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