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I was reading Urs Schreiber's 'Higher Topos Theory', and he casually points out how quantum physics (being a linear theory) is given by probing a space via negative dimensional spheres in stable homotopy theory.
Are there any good resources on stable homotopy theory for someone unfamiliar with the stable homotopy theory and these negative spheres?
You could start with Rok Gregoric' Spectra are your Friends: https://web.ma.utexas.edu/users/gregoric/Spectra%20Are%20Your%20Friends.pdf
That looks fun!