This is the first of a series of two articles where we construct a version of wrapped Fukaya category $\mathcal W\mathcal F(M\setminus K;H_{g_0})$ of the cotangent bundle $T^*(M \setminus K)$ of the knot complement $M \setminus K$ of a compact 3-manifold $M$, and do some calculation for the case of hyperbolic knots $K \subset M$. For the construction, we use the wrapping induced by the kinetic energy Hamiltonian $H_{g_0}$ associated to the cylindrical adjustment $g_0$ on $M \setminus K$ of a smooth metric $g$ defined on $M$... (read more)

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