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Morse theory on Banach manifolds

1970
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Bulletin of the American Mathematical Society
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Let f be a C2 function on a C2 Banach manifold. A critical point x off is said to be weakly nondegenerate if there exists a neighborhood 7J of x and a hyperbolic linear isomorphism L, : T,(M) --, T,(M) such that in the coordinate system of U, df,+,(Lp) > 0 if v # 0. L, defines an index invariantly, and it is shown that this is an extension of the usual definition of nondegeneracy and index. It is shown that this weaker nondegeneracy can be used in place of the stronger nondegeneracy conditions

doi:10.1090/s0002-9904-1970-12384-9
fatcat:qfnianhtcbh4hhymyxc2molfnu