Date: Wed, 20 Jan 1999 11:05:08 +0900
From: Andrzej Kozlowski <andrzej@tuins.ac.jp>
Subject: Re: htpy gps of spheres

On Tue, Jan 19, 1999, DON DAVIS <dmd1@Lehigh.EDU> wrote:

>Date: Wed, 20 Jan 1999 01:23:22 GMT
>From: carlos@picard.ups-tlse.fr (Carlos Simpson)
>Subject: Re: response to R. Brown
>
>As predicted by Andrzej Kozlowski, ``the study of well-defined things''
>does seem like a good answer. This provides an occasion to post to the
>topology list, where it belongs, a question raised a while ago on
>``categories'' (my apologies to the probably large number of you who
>subscribe to both lists).
>
>To be brief: it is often stated that ``one of the major problems in topology
>is the homotopy groups of spheres''. What is the ``well-defined'' question
>here? For example, is there an explicit conjecture that needs to be proved?
>
>---Carlos Simpson
>
>
>
>

I am sure I am biased, but it seems to me that the only "well defined"
problem in this area that I can think of is dead. It was killed by David
Anick's proof that the problem of computing the homotopy groups of
spheres is of the  NP-complete type, which essentially means that
algorithms are useless for this purpose. In spite of this  I still, from
time to time, find myself attending talks (the last time a couple of
moths ago) where people present yet another totally impractical one. Of
course all the answers are somewhere in the Platonic universe of correct
answers to all mathematical problems (except, perhaps, the undecidable
ones), but we just can't get at them.

Andrzej Kozlowski

Toyama International University
JAPAN
http://sigma.tuins.ac.jp/
http://eri2.tuins.ac.jp/