Subject: Re: two responses From: James Stasheff Date: Wed, 23 Mar 2005 15:39:10 -0500 (EST) To: Don Davis Thanks I as trying to be provocative (cf. Larry Summers) expecting an answer in terms of conditions on k in terms of n_i, m Jim Stasheff jds@math.upenn.edu Home page: www.math.unc.edu/Faculty/jds As of July 1, 2002, I am Professor Emeritus at UNC and I will be visiting U Penn but for hard copy the relevant address is: 146 Woodland Dr Lansdale PA 19446 (215)822-6707 On Wed, 23 Mar 2005, Don Davis wrote: >> Two responses to yesterday's question...........DMD >> ______________________________________________________________ >> >> Subject: Re: three postings >> From: "Prof. A. R. Shastri" >> Date: Wed, 23 Mar 2005 10:03:20 +0530 (IST) >> >> I think Jim forgot to tell us that the (expletive withheld) >> k (dimension of P) should satisfy the condition k+n_i> statement is false. With the above assumption, it follows by >> relative version of transversality. >> >> Anant R. Shastri >> ars@math.iitb.ac.in >> >> >> Subject: query >> >> From: James Stasheff >> >> Date: Tue, 22 Mar 2005 08:44:37 -0500 (EST) >> >> >> >> Query: >> >> Is the following ( or something similar) a therem inthe literature? >> >> note I am old enough to write M - N for the complement of N \subset M >> >> instead of the (expletive delted) M\N >> >> >> >> Let M be a smooth manifold of dim m >> >> N a closed submanifold with components N_i of dims n_i >> >> If P is a compact smooth manifold of dim k with non-trivial boundary >> >> and f : P --> M with \partial P --> M-N >> >> then f can be deformed off N keeping \partial P fixed >> >> ?? >> >> >> _____________________________________________________________ >> >> Subject: RE: three postings >> From: "Lynn Dover" >> Date: Wed, 23 Mar 2005 10:34:31 -0700 >> >> Jim: >> >> Unless I have mis-understood your question, your statement is false. >> Consider, for example, >> >> M = standard 2-sphere >> N = the circle at the equator >> P = the unit disk >> f maps P in the expected way onto the top 2/3 of the sphere (hence covering >> N with the boundary of P ending up "below" N) >> >> There is no way to deform f off of N while fixing the boundary of f(P). >> >> Hope this helps. >> >> Lynn Dover >> Department of Mathematical and Statistical Sciences >> University of Alberta >> Edmonton, Canada >>