When is a map essential in Čech cohomology?

I read a nice survey of parts of game theory, Foundations of Strategic Equilibrium, by Hillas and Kohlberg. Something where I stumble is the discussion of Mertens stability. There is a definition that requires a certain map to be essential in Čech cohomology and I know nothing about cohomology. So I would like to know:

Is there a self-contained way to define essentiality of a map in Čech cohomology that can be explained to someone who knows point-set topology quite well but knows almost nothing about algebraic topology? If yes, please give the definition and maybe a bit of explanation..

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What means "to be essential in Čech cohomology"? – Boris Novikov Mar 5 '13 at 7:45
@BorisNovikov That is the question. The whole thing appears at the end of page 45 and beginning of page 46 in the linked text. – Michael Greinecker Mar 5 '13 at 15:27
Thank you, I try to understand. – Boris Novikov Mar 5 '13 at 16:17

Hillas has an excellent working paper where you can get a nice intuition of what such an essentiality condition implies. The title is "A Game Illustrating Some Features of the Definition of Strategic Stability".

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I found the paper where a correct definition of essentiality is given:

Srihari Govindan and Jean-Francois Mertens (1993): \An Equivalent Def- inition of Stable Equilibria"

If you want I will send it by e-mail. As to Cech cohomology, there is the classical book

Spanier, Ediwin H (1966) Algebraic Topology. McGraw Hill, New York.

However it is very thick. I can recommend, e.g.,

Morgan J. W., Lamberson P. J. Algebraic Topology

(I can send it also; though I didn't read it).

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