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For finite dimensional manifolds, there is a lot of theory about when the number of intersections (modulo $2$) of certain objects are preserved under homotopy. I'll give two quick examples: Let $f:X \...

I originally posted this question on StackExchange, where it was suggested I post here. It was also suggested I read about Hilbert manifolds and Fréchet manifolds. Nevertheless, I am still looking for ...