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What are applications of spin geometry to physics? Does it have something to do with gravity?

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    $\begingroup$ Applications to what? Math? Physics? Chemistry? $\endgroup$
    – Moishe Kohan
    Commented Feb 6, 2023 at 20:33
  • $\begingroup$ Applications to physics. $\endgroup$
    – Tianyu Yuan
    Commented Feb 6, 2023 at 20:48

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I understand the question as requesting applications of the geometry of spin manifolds outside of pure mathematics. There are many, starting with the Dirac equation for the spinor of a relativistic electron (1920). Recent applications center on topological states of matter and on quantum theories of gravity.

One recent overview is given in Spin Geometry and Some Applications.

For an application beyond physics, see Spin Geometry and Image Processing.

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  • $\begingroup$ Thank you very much. $\endgroup$
    – Tianyu Yuan
    Commented Feb 6, 2023 at 20:49

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