The so called Leray-Schauder degree is usually defined for maps of the form $I - f$, where $f: X \to X$ is a compact map defined on a Banach space. Is there an extended definition for the setting of Banach manifolds?
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$\begingroup$ The book "Topological analysis" by Martin Väth might have the information you are looking for; see Zbl 1248.47001. $\endgroup$– Dirk WernerCommented Sep 8, 2021 at 21:41
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