The Viterbo Transfer as a Map of Spectra

الأصل · EN

Let L and N be two smooth manifolds of the same dimension. Let j L→ T*N be an exact Lagrange embedding. We denote the free loop space of X by ΛX. C. Viterbo constructed a transfer map (Λj)! H*(ΛL) → 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)! (ΛN)-TN → (ΛL)-TL+η, where η is a virtual vector bundle classified by the tangential information of j.