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Have derived algebraic geometry been used to understand the topology of complex varieties? For example are there any applications in Morse theory?

The reason I am asking this is two fold. First one is the derived scheme entry on Wikipedia. There is a section for applications in Morse theory. It claims that DAG can be used to understand the topology of affine varieties but what follows after that is extremely underwhelming. So this left me wondering whether there is more to this or not? Are there new proofs for known topological facts or new topological facts that their statement does not depend on DAG but have been proved using DAG?

The second one is this paper by David Kern, which he gives a generalization/categorical version of quantum Lefschetz. He later on derives the classical version from it. Although the quantum Lefschetz is an algebraic statement regarding $G$-theory and there is not much topology in it, I am wondering now whether one can use DAG to give a different proof of something like Lefschetz hyperplane theorem? Or some generalization of it with relaxed conditions. Is something like this known or not? (Of course there is the intersection homology version, that is not what I mean.)

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    $\begingroup$ You might also look at Kapranov-Vasserot. $\endgroup$
    – Jason Starr
    Commented Jan 19, 2022 at 0:37
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    $\begingroup$ As phrased, the Wikipedia claim is somewhat suspect. What the section on Morse theory is hinting at is that derived geometry provides a conceptual explanation of certain "enhancements" of spaces that appear as critical loci. So derived geometry is related to things like virtual fundamental classes and Floer homology. (You don't really need derived geometry these, but it provides a nice framework). $\endgroup$
    – user41282141
    Commented Jan 19, 2022 at 3:49

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