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maps and thus descend to the same isomorphism on homology. However, in certain infinite dimensional cases, this does not hold, and these techniques may be used to produce invariants of one-parameter families of objects (such as
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in infinite dimensional analogues of the situation described above; in the case of finite-dimensional Morse theory, invariance may be proved by proving that Morse homology is isomorphic to
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Lecture Notes on Morse
Homology (including continuation maps in finite-dimensional theory), by Michael Hutchings
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In finite-dimensional Morse theory, different choices made in constructing the vector field on
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Contact homology and homotopy groups of the space of contact structures by
Frederic Bourgeois
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Contact homology and one parameter families of
Legendrian knots by Tamas Kalman
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