Given two principal Diff-bundles: (p1,2 , E(A1,2 , M) , B1,2) where E(- , -) is the space of smooth embeddings with the structure group Diff(A1) is a closed subgroup of Diff(A2). I've proved that E(A1 , M) and E(A2 , M) are homotopy equivalent. I assume(if I am not mistaken) that the base spaces B= E(A1,2 , M)/Diff(A1,2) are homotopy equivalent too. I do not know how to prove these bundles are isomorphic, i.e., there exist diffeomorphisms makes the principal bundles commute.
Cenap Özel
dear Sakita
check S Lang Differentual geometry or Hirch Diff Topology u can find all details..
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