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In differential topology, Morse theory enables one to analyze the topology of a manifold by studying differentiable functions on that manifold.

2 votes

Gluing in Morse homology for Hilbert manifolds

I would say, take a look at the paper of Abbondandolo and Majer :http://arxiv.org/abs/math/0403552 or http://www.dm.unipi.it/~abbondandolo/preprints/montreal.pdf The construction is neat and clear.
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