What is the connection between critical points of a functional over an infinite dimensional Banach space and a critical group at that point?. For instance, I was wondering as to what is the significance of computing the critical group $C^q(I,u)=H^q(I^c\cap U,I^c\cap U\setminus\{u\})$, $q\geq 0$?. Here $I$ is the $C^1$ functional over the Banach space $X$, $I^c=\{v:I(v)\leq c\}$, $U$ is a neighbourhood of the critical point $u\in X$.
2026-03-27 11:24:35.1774610675
Homology group for critical points
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The clarity was already provided. The link you provided has the clearer version of the question. The older question didn't have the mathematical detail in it. The older version just had "What is the connection between critical points of a functional over an infinite dimensional Banach space and a critical group at that point?."