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- W3040694386 abstract "Conceptually, the goal here is a construction which functorially translates a Hamiltonian fibre bundle to a certain ``derived vector bundle'' over the same space, with fiber an $A _{infty} $ category. This ``derived vector bundle'' must remember the continuity of the original bundle. Concretely, using Floer-Fukaya theory for a monotone $(M, omega)$ we construct a natural continuous map begin{equation*} BHam (M, omega) to (mathcal{S}, NFuk (M)), end{equation*} with $(mathcal{S}, NFuk (M))$ denoting the $NFuk (M)$ component of the ``space'' of $infty$-categories, where $NFuk (M)$ is the $A _{infty} $-nerve of the Fukaya category $Fuk (M)$. This construction is very closely related to the theory of the Seidel homomorphism and the quantum Chern classes of the author, and this map is intended to be the deepest expression of their underlying geometric theory. In part II the above map is shown to be non trivial by an explicit calculation. In particular we arrive at a new non-trivial ``quantum'' invariant of any smooth manifold and a ``quantum'' Novikov conjecture." @default.
- W3040694386 created "2020-07-16" @default.
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- W3040694386 date "2013-07-15" @default.
- W3040694386 modified "2023-10-11" @default.
- W3040694386 title "Global Fukaya category and quantum Novikov conjecture I" @default.
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