From: Dan Christensen <jdc@jhu.edu>
Subject: Re: Triangulations of n-spheres
Date: Fri, 14 Jan 2000 19:08:24 -0500
Newsgroups: sci.math.research
Summary: [missing]

Rob Arthan <rda@lemma-one.com> writes:
> [For k at most n and any cellular decomposition of the n-sphere,] 
> is it true that the inclusion of the (k-1)-skeleton of an n-sphere
> in the k-skeleton is null-homotopic?

Yes.  First, note that the inclusion of the (k-1)-skeleton into the
n-sphere is null.  (E.g. use the cellular approximation theorem for
the trivial cell-decomposition of the n-sphere with only two cells.)
Then the cellular approximation theorem tells you that a null homotopy
can be found that factors through the k-skeleton.

Dan

-- 
Dan Christensen
jdc@math.jhu.edu