Re: Uniqueness of Solutions to the Relative Lifting Problem

Hello, all!

I have been helped by Ross Geoghegan of Binghamton University, who
suggested the obstruction theory chapter of _Homology Theory_ by Hilton
& Wylie (Peter Hilton also being of Binghamton University).

_Homology Theory_ in turn led me to "Obstructions to Extensions and
Homotopies" by Paul Olum. I cannot recommend this paper strongly enough
for the beginner. It's a little light on examples, but the exposition is
unparalleled. If you want a nickel's worth of free advice, stay away
from Hatcher's exposition. His excursion into Postinikov towers is
misleading for the beginner.

Hope this helps. I just wanted to record this for posterity.

Sincerely,
--
Jeffrey Rolland
<wildstar200@xxxxxxxxxxx>

In article <fso859$hmm$1@xxxxxxxxxxxxxxxx>,
Jeffrey Rolland <wildstar200@xxxxxxxxxxx> wrote:

Hello, all!

I am stuck trying to do a relative lifting problem.

The basic premise is, I have two 8-dimensional (well, the domain is
8-dim'l and the range is infinite dimensional, but all maps are to be
cellular, so the range may as well be 8-dim'l) (both have finitely many
cells in each dimension) CW complexes, and I would like to find all
homotopy classes of maps between them.

<snip>

Additionally, if someone knows the set of homotopy classes of maps between
closed, orientable surfaces (the sphere to the torus, the torus to the
torus, the torus to the the double-torus, the double-torus to the sphere,
etc.), and how to derive these sets from data like the standard CW
decompositions of the closed, orientable surfaces and perhaps their
homology and/or homotopy groups, that would be tremendously helpful.

(Of couse, the set of homotopy classes of maps of the sphere to the sphere
I know :))

Thank you in advance for any assistance you can provide.

Sincerely,

.