Orbifold Quantum Cohomology, Gromov–Witten Theory and the Quantum-Product

In physics, you don't have to go around making trouble for yourself - nature does it for you ~ Frank Wilczek ... Why I always say: 'lucky we have mathematicians'

In my last four posts, I derived two propositions about quantum cohomology, with mirror-symmetry for Calabi-Yau manifolds being an isomorphism of variations of Hodge structures, with the A-model, defined by the genus zero Gromov–Witten theory of X , isomorphic to the B-model of variations of Hodge structures associated to deformation of complex structures of the mirror Y

Gromov–Witten Theory, Quantum Cohomology and Mirror Symmetry

"It was mathematics, the non-empirical science par excellence, wherein the mind appears to play only with itself, that turned out to be the science of sciences, delivering the key to those laws of nature and the universe that are concealed by appearances" ~ Hannah Arendt

In this post, I will begin the first part of a study of the cohomological-Dubrovin connection in the context of mirror-symmetry for Calabi-Yau Gromov–Witten theory. In particular, I will derive two propositions about quantum cohomology. In my last three posts, I finally derived, after studying the Witten Equation as well as the Landau-Ginzburg/Calabi-Yau correspondence, the Witten super-Dubrovin compactification Chern-Simons formula

The Witten Super-Dubrovin 'Compactification Chern-Simons' Formula

“But in my opinion, all things in nature occur mathematically” ~ René Descartes

In my last two posts on the Witten Equation, I showed that in the context of Picard-Lefschetz Theory, it entails the non-forking, super-stability and hyper-categoricity of M-theory, making it, up to isomorphism, the only unification theory possible between Einstein's ToGR and Quantum Field Theory, as well as derived the Dubrovin connection and related it to Kähler-Witten integral and showed that it is a necessary condition for the action-principle of any such unified 'Theory-of-Everything'. Let's delve deeper.