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Let $S$ be the sphere spectrum, and for $X$ a topological space, let $S(X)$ be the mapping spectrum from the free loop spectrum on $X$ to the sphere spectrum. This is an $E_\infty$ ring spectrum (also ...

I am currently trying to wrap my head around all kinds of different definitions of the notion of (generalized) Thom spectrum. My setup is as follows: Suppose I have a commutative (symmetric) ring ...