The Viterbo Transfer as a Map of Spectra

Let $L$ and $N$ be two smooth manifolds of the same dimension. Let $j\colon L\to T^*N$ be an exact Lagrange embedding. We denote the free loop space of $X$ by $ΛX$. C. Viterbo constructed a transfer map $(Λj)^! \colon H^*(ΛL) \to H^*(ΛN)$. This transfer was constructed using finite dimensional approximation of Floer homology. In this paper we define a family of finite dimensional approximations and realize this transfer as a map of Thom spectra: $(Λj)_! \colon (ΛN)^{-TN} \to (ΛL)^{-TL+η}$, where $η$ is a virtual vector bundle classified by the tangential information of $j$.

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