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In a paper of P. MichorP. Michor, it was shown that Emb(M,N) is a smooth principal diff(M)-bundle, M and N are smooth locally compact manifolds provided dim M < dim N. My question is why there is a restriction on the dimensions. Does anyone know a reference for the result when dim M = dim N ?

Thanks in advance

In a paper of P. Michor, it was shown that Emb(M,N) is a smooth principal diff(M)-bundle, M and N are smooth locally compact manifolds provided dim M < dim N. My question is why there is a restriction on the dimensions. Does anyone know a reference for the result when dim M = dim N ?

Thanks in advance

In a paper of P. Michor, it was shown that Emb(M,N) is a smooth principal diff(M)-bundle, M and N are smooth locally compact manifolds provided dim M < dim N. My question is why there is a restriction on the dimensions. Does anyone know a reference for the result when dim M = dim N ?

Thanks in advance

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s k
s k
  • 111
  • 3

The principal bundle of embeddings

In a paper of P. Michor, it was shown that Emb(M,N) is a smooth principal diff(M)-bundle, M and N are smooth locally compact manifolds provided dim M < dim N. My question is why there is a restriction on the dimensions. Does anyone know a reference for the result when dim M = dim N ?

Thanks in advance