Date: Thu, 29 Apr 1999 13:10:02 -0400 (EDT)
From: Jie Wu <jiewu@math.upenn.edu>
Subject: Size of homotopy groups

The following questions were asked by Wolfgang Ziller:

Are there any descriptions about the size (order) t(k) of \pi_k(S^n)?

Is  t(k) bounded by an exponential function on k, a polynomial function on
k or even better?

To my understanding, the size of homotopy groups can be used by them to
solve some problems in differential geometry if the size has a good upper
bound.

I would like to ask the following related question:

Are there any descriptions about the upper bound of the Poincare series of
E^2-terms (or higher terms) in the Adams spectral sequences?

(This may give them some information about the  size of homotopy groups).

Another question they asked is:

Can we say anything about \pi_k(S^n)\otimes \Z/p?

Best Regards,

Jie


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Jie Wu

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