Subject: question for discussion list
Date: Wed, 2 Oct 2002 17:54:27 -0700 (PDT)
From: Igor Belegradek <ibeleg@its.caltech.edu>
To: dmd1@lehigh.edu

Dear Professor Davis,

Could you post the following question for the Topology
discussion list?

Let M be a boundary component of a cobordism W such that the
inclusion M-->W is r-connected. It is known that if r<dim(W)-3,
then W can be obtained from M x I by attaching handles of
indices >r.

(See e.g. C. T. C. Wall, Geometrical connectivity I, J. London.
Math. Society., 3, (1971), 597-604).

Is the bound r<dim(W)-3 optimal? I am especially interested in
the case r=1, dim(W)=4, but I wish to know about higher
dimensions as well.

Thank you very much,

Igor Belegradek
ibeleg@caltech.edu