Lectures on the Eilenberg-Moore Spectral Sequence
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134 Larry Smith University of Virginia, Dept. of Mathematics Charlottesville, VA/USA
Lectures on the Eilenberg-Moore Spectral Sequence
Springer-Verlag Berlin· Heidelberg· New York 1970
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To Mi -Soo
Introduction These notes are an outgrowth of lectures that I delivered during the spring of
1969
at
Aarhus
University.
They represent
my feeble attempts to organize in a coherent way the circle of ideas revolving about the spectral sequence introduced by Eilenberg and
Moore in
[18]. The first part of these notes
presents a new construction for the spectral sequence based on viewing it as a the category
Kunneth spectral sequence in a suitable category,
Top/B
of spaces over a fixed space
has also been employed by appeared in print.
B.
This idea
L. Hodgkin whose work has not yet
The category
Top/S
and its pointed analog
offer a suitable setting for many other ideas, constructions and theorems. [19]
We reccomend that the interested reader consult
[23] [28] [33] and/or [45]
[8]
for further material in this
direction. The second part of these notes deals with a situation in which the
Eilenberg-Moore spectral sequence has proved most
tractable.
the study of stable
Postnikov systems.
Most,
if not all , of the material of this section is an outgrowth of my joint published
[31] and unpublished work with J.e.Moore.
I have tried to collect and clarify the results that are spread through
[31],[38J, [39], and
problem, namely how does the depend on the nUmber of
[44]
as they apply to a particular
Pontrjagin ring of a
k-invariants.
Hopf space
These same ideas and
techniques have proven useful in other -related situations for example
(see
[37],[40],[41]) and it is hoped they will commend
themselves to further study.
VI The third part of these lectures is concerned with several results that may be obtained from the precursor to the Moore spectral sequence introduced by
J.F. Adams in
Eilenberg[1].
Many
of the results we discuss in this part are an outgrowth of my unpublished work with
Alan Clark.
I believe that these results
have been known to the experts for some time.
They demonstrate
the distinct advantage to be obtained form the algebraic approach of
[1] and
[18]
in certain situations.
There are individual introductions to the three separate parts of these notes and we refer to them for a more detailed summary of the material covered. I would like to express thanks to my many col
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