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I have this paragraph from K.C. Chang Infinite dimensional Morse theory
In comparison with degree theory, which has proved very useful in nonlinear analysis in proving existence and in estimating the number of solutions to an operator equation, Morse theory has a great advantage if the equation is variational. Relative homology groups and critical groups are series of groups that provide both a finer structure and better estimate of the number of solutions than does the degree, which is only an integer. The relationship between the Leray-Schauder index and critical groups is established.
And I don't Understand how to see that Morse theory is better then degree theory,
how to see that Relative homology groups and critical groups provide both a finer structure and better estimate of the number of solutions than does the degree ?
Please help me