The Viterbo Transfer as a Map of Spectra

2007/12/17 by Kragh, Thomas
#53D12 #53D25 #53D40 #57R17 #Algebraic Topology (math.AT) #FOS: Mathematics #Symplectic Geometry (math.SG)

paper · doi:10.48550/arxiv.0712.2533

Abstract

Let L and N be two smooth manifolds of the same dimension. Let j\colon 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)^! \colon 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)_! \colon (ΛN)^-TN → (ΛL)^-TL+η, where η is a virtual vector bundle classified by the tangential information of j.

Related

• The transfer map of free loop spaces
• Symplectic cohomology and Viterbo's theorem
• Viterbo's spectral bound conjecture for homogeneous spaces
• The Floer homotopy type of the cotangent bundle
• Spectra of differentiable hyperbolic maps