2021/09/09 by Wenran Liu, Liu, Wenran
Mathematics · #Advanced Topology and Set Theory #Homotopy and Cohomology in Algebraic Topology #Geometric and Algebraic Topology
paper · pdf · doi:10.48550/arxiv.2109.04005
The group of diffeomorphisms commuting with an elliptic operator on a manifold is a compact Lie group under Compact-Open topology. In foliation theory, pseudogroup is introduced by Sacksteder. The pseudogroup of local transformations commuting with a basic differential operator possesses the equicontinuity and the quasi-analyticity when conditions on operator are given. These properties serve to construct a transverse metric on the normal bundle under a good condition on operator. For this, the Average Method is applied as in the construction of basic connection on foliated bundles.