2011/08/01 by Jungsoo Kang, Kang, Jungsoo
Mathematics · #46C99 #53D99 #FOS: Mathematics #Symplectic Geometry (math.SG) #math.SG #msc:46C99 #msc:53D99
paper · pdf · doi:10.48550/arxiv.1108.0327
14 pages
arxiv created 2011/08/01 · arxiv updated 2011/08/02
Scale structures were introduced by H. Hofer, K. Wysocki, and E. Zehnder as a new concept of a smooth structure in infinite dimensions. We prove that scale structures on mapping spaces are completely determined by the dimension of domain manifolds. As a consequence, we give a complete description of the local invariant introduced by U. Frauenfelder for mapping spaces. Product mapping spaces and relative mapping spaces are also studied. Our approach is based on the spectral resolution of Laplace type operators together with the eigenvalue growth estimate.