Subject: Re: two postings From: Tom Goodwillie Date: Mon, 28 Mar 2005 16:05:41 -0500 To: Don Davis > > > I find Tom Goodwille's repsonse interesting. Once again, > I believe the result he described must be true if > k k Anant Shastri I said 2m-n_1-n_2-2 .This is the same number you would get if you looked at smooth or continuous maps instead of emneddings. In the diagram M - (N_1UN_2) ---> M - N_1 | I v v M - N_2 ---> M the map from the upper left space to the homotopy pullback of the other three is a (2m - n_1 - n_2 - 3)-connected map. It follows easily that the diagram of function spaces obtained by applying (Map(P,-) to all the manifolds is such that now the map from the upper left space to the homotopy pullback of the other three is a (2m - n_1 - n_2 - 3 - k)-connected map if P is k-dimensional. It is also true, but harder to prove, for embeddings. TG